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molality = nsolute / msolvent
nsolute = msolute / Msolute
where nsolute is in moles, msolvent is in kg, msolute is in g, and Msolute is in g/mol

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Visualization of a solution with 10 g of solute in 1 kg of solvent, resulting in a molality of unknown mol/kg.
๐Ÿ“š

ืชื™ืขื•ื“

ืžื—ืฉื‘ื•ืŸ ืžื•ืœืœื™ื•ืช: ื—ื™ืฉื•ื‘ ืจื™ื›ื•ื– ืคืชืจื•ืŸ

ืžื‘ื•ื

ืžื—ืฉื‘ื•ืŸ ื”ืžื•ืœืœื™ื•ืช ื”ื•ื ื›ืœื™ ืžื“ื•ื™ืง ื•ื™ื“ื™ื“ื•ืชื™ ืœืžืฉืชืžืฉ, ืฉื ื•ืขื“ ืœื—ืฉื‘ ืืช ื”ืžื•ืœืœื™ื•ืช ืฉืœ ืคืชืจื•ื ื•ืช ื›ื™ืžื™ื™ื. ืžื•ืœืœื™ื•ืช (ืžืกื•ืžื ืช ื›-'m') ื”ื™ื ื™ื—ื™ื“ืช ืจื™ื›ื•ื– ื—ืฉื•ื‘ื” ื‘ื›ื™ืžื™ื”, ื”ืžื•ื“ื“ืช ืืช ืžืกืคืจ ื”ืžื•ืœื™ื ืฉืœ ื”ืžื•ืžืก ืœื›ืœ ืงื™ืœื•ื’ืจื ืฉืœ ืžืžืก. ื‘ื ื™ื’ื•ื“ ืœืžื•ืœืจื™ื•ืช, ืฉืžืฉืชื ื” ืขื ื”ื˜ืžืคืจื˜ื•ืจื” ื‘ืฉืœ ืฉื™ื ื•ื™ื™ื ื‘ื ืคื—, ื”ืžื•ืœืœื™ื•ืช ื ืฉืืจืช ืงื‘ื•ืขื” ืœืœื ืงืฉืจ ืœืฉื™ื ื•ื™ื™ื ื‘ื˜ืžืคืจื˜ื•ืจื”, ืžื” ืฉื”ื•ืคืš ืื•ืชื” ืœื™ืงืจื” ื‘ืžื™ื•ื—ื“ ืœื—ื™ืฉื•ื‘ื™ื ืชืจืžื•ื“ื™ื ืžื™ื™ื, ืžื—ืงืจื™ ืชื›ื•ื ื•ืช ืงื•ืœื™ื’ื˜ื™ื‘ื™ื•ืช, ื•ื”ื›ื ื•ืช ืžืขื‘ื“ืชื™ื•ืช ื”ื“ื•ืจืฉื•ืช ืžื“ื™ื“ื•ืช ืจื™ื›ื•ื– ื‘ืœืชื™ ืชืœื•ื™ื•ืช ื‘ื˜ืžืคืจื˜ื•ืจื”.

ืžื—ืฉื‘ื•ืŸ ื–ื” ืžืืคืฉืจ ืœืš ืœืงื‘ื•ืข ื‘ืžื“ื•ื™ืง ืืช ื”ืžื•ืœืœื™ื•ืช ืฉืœ ืคืชืจื•ืŸ ืขืœ ื™ื“ื™ ื”ื–ื ืช ืžืกืช ื”ืžื•ืžืก, ืžืกืช ื”ืžืžืก, ื•ืžืกืช ื”ืžื•ืœืœ ืฉืœ ื”ืžื•ืžืก. ืขื ืชืžื™ื›ื” ื‘ืžื’ื•ื•ืŸ ื™ื—ื™ื“ื•ืช ืžืกื” (ื’ืจืžื™ื, ืงื™ืœื•ื’ืจืžื™ื, ื•ืžื™ืœื™ื’ืจืžื™ื), ืžื—ืฉื‘ื•ืŸ ื”ืžื•ืœืœื™ื•ืช ืžืกืคืง ืชื•ืฆืื•ืช ืžื™ื™ื“ื™ื•ืช ืœืกื˜ื•ื“ื ื˜ื™ื, ื›ื™ืžืื™ื, ืจื•ืงื—ื™ื, ื•ื—ื•ืงืจื™ื ื”ืขื•ื‘ื“ื™ื ืขื ื›ื™ืžื™ื” ืฉืœ ืคืชืจื•ื ื•ืช.

ืžื”ื™ ืžื•ืœืœื™ื•ืช?

ืžื•ืœืœื™ื•ืช ืžื•ื’ื“ืจืช ื›ืžืกืคืจ ื”ืžื•ืœื™ื ืฉืœ ื”ืžื•ืžืก ื”ืžื•ืžืกื™ื ื‘ืงื™ืœื•ื’ืจื ืื—ื“ ืฉืœ ืžืžืก. ื”ื ื•ืกื—ื” ืœืžื•ืœืœื™ื•ืช ื”ื™ื:

m=nsolutemsolventm = \frac{n_{solute}}{m_{solvent}}

ืื™ืคื”:

  • mm ื”ื™ื ื”ืžื•ืœืœื™ื•ืช ื‘ืžื•ืœ/ืง"ื’
  • nsoluten_{solute} ื”ื•ื ืžืกืคืจ ื”ืžื•ืœื™ื ืฉืœ ื”ืžื•ืžืก
  • msolventm_{solvent} ื”ื™ื ืžืกืช ื”ืžืžืก ื‘ืงื™ืœื•ื’ืจืžื™ื

ืžืื—ืจ ืฉืžืกืคืจ ื”ืžื•ืœื™ื ืžื—ื•ืฉื‘ ืขืœ ื™ื“ื™ ื—ืœื•ืงืช ืžืกืช ื—ื•ืžืจ ื‘ืžืกืช ื”ืžื•ืœืœ ืฉืœื•, ื ื•ื›ืœ ืœื”ืจื—ื™ื‘ ืืช ื”ื ื•ืกื—ื” ืœ:

m=msolute/Msolutemsolventm = \frac{m_{solute}/M_{solute}}{m_{solvent}}

ืื™ืคื”:

  • msolutem_{solute} ื”ื™ื ืžืกืช ื”ืžื•ืžืก
  • MsoluteM_{solute} ื”ื™ื ืžืกืช ื”ืžื•ืœืœ ืฉืœ ื”ืžื•ืžืก ื‘ื’ืจื/ืžื•ืœ
  • msolventm_{solvent} ื”ื™ื ืžืกืช ื”ืžืžืก ื‘ืงื™ืœื•ื’ืจืžื™ื

ื›ื™ืฆื“ ืœื—ืฉื‘ ืžื•ืœืœื™ื•ืช

ืžื“ืจื™ืš ืฉืœื‘-ืื—ืจ-ืฉืœื‘

  1. ืงื‘ืข ืืช ืžืกืช ื”ืžื•ืžืก (ื”ื—ื•ืžืจ ื”ืžื•ืžืก)

    • ืžื“ื•ื“ ืืช ื”ืžืกื” ื‘ื’ืจืžื™ื, ืงื™ืœื•ื’ืจืžื™ื, ืื• ืžื™ืœื™ื’ืจืžื™ื
    • ื“ื•ื’ืžื”: 10 ื’ืจื ืฉืœ ื›ืœื•ืจื™ื“ ื ืชืจืŸ (NaCl)
  2. ื–ื”ื” ืืช ืžืกืช ื”ืžื•ืœืœ ืฉืœ ื”ืžื•ืžืก

    • ื—ืคืฉ ืืช ืžืกืช ื”ืžื•ืœืœ ื‘ื’ืจื/ืžื•ืœ ืžื”ื˜ื‘ืœื” ื”ืžื—ื–ื•ืจื™ืช ืื• ืžื”ื”ืคื ื™ื” ื”ื›ื™ืžื™ืช
    • ื“ื•ื’ืžื”: ืžืกืช ื”ืžื•ืœืœ ืฉืœ NaCl = 58.44 ื’ืจื/ืžื•ืœ
  3. ืžื“ื•ื“ ืืช ืžืกืช ื”ืžืžืก (ื‘ื“ืจืš ื›ืœืœ ืžื™ื)

    • ืžื“ื•ื“ ืืช ื”ืžืกื” ื‘ื’ืจืžื™ื, ืงื™ืœื•ื’ืจืžื™ื, ืื• ืžื™ืœื™ื’ืจืžื™ื
    • ื“ื•ื’ืžื”: 1 ืงื™ืœื•ื’ืจื ืฉืœ ืžื™ื
  4. ื”ืžืจ ืืช ื›ืœ ื”ืžื“ื™ื“ื•ืช ืœื™ื—ื™ื“ื•ืช ืชื•ืืžื•ืช

    • ื•ื“ื ืฉืžืกืช ื”ืžื•ืžืก ื”ื™ื ื‘ื’ืจืžื™ื
    • ื•ื“ื ืฉืžืกืช ื”ืžืžืก ื”ื™ื ื‘ืงื™ืœื•ื’ืจืžื™ื
    • ื“ื•ื’ืžื”: 10 ื’ืจื NaCl ื•-1 ืงื™ืœื•ื’ืจื ืžื™ื (ืื™ืŸ ืฆื•ืจืš ื‘ื”ืžืจื”)
  5. ื—ืฉื‘ ืืช ืžืกืคืจ ื”ืžื•ืœื™ื ืฉืœ ื”ืžื•ืžืก

    • ื—ืœืง ืืช ืžืกืช ื”ืžื•ืžืก ื‘ืžืกืช ื”ืžื•ืœืœ ืฉืœื•
    • ื“ื•ื’ืžื”: 10 ื’ืจื รท 58.44 ื’ืจื/ืžื•ืœ = 0.1711 ืžื•ืœ ืฉืœ NaCl
  6. ื—ืฉื‘ ืืช ื”ืžื•ืœืœื™ื•ืช

    • ื—ืœืง ืืช ืžืกืคืจ ื”ืžื•ืœื™ื ืฉืœ ื”ืžื•ืžืก ื‘ืžืกืช ื”ืžืžืก ื‘ืงื™ืœื•ื’ืจืžื™ื
    • ื“ื•ื’ืžื”: 0.1711 ืžื•ืœ รท 1 ืง"ื’ = 0.1711 ืžื•ืœ/ืง"ื’

ืฉื™ืžื•ืฉ ื‘ืžื—ืฉื‘ื•ืŸ ื”ืžื•ืœืœื™ื•ืช

ืžื—ืฉื‘ื•ืŸ ื”ืžื•ืœืœื™ื•ืช ืฉืœื ื• ืžืคืฉื˜ ืืช ื”ืชื”ืœื™ืš ื”ื–ื”:

  1. ื”ื›ื ืก ืืช ืžืกืช ื”ืžื•ืžืก
  2. ื‘ื—ืจ ืืช ื™ื—ื™ื“ืช ื”ืžื“ื™ื“ื” ืขื‘ื•ืจ ื”ืžื•ืžืก (ื’ืจื, ืง"ื’, ืื• ืž"ื’)
  3. ื”ื›ื ืก ืืช ืžืกืช ื”ืžืžืก
  4. ื‘ื—ืจ ืืช ื™ื—ื™ื“ืช ื”ืžื“ื™ื“ื” ืขื‘ื•ืจ ื”ืžืžืก (ื’ืจื, ืง"ื’, ืื• ืž"ื’)
  5. ื”ื›ื ืก ืืช ืžืกืช ื”ืžื•ืœืœ ืฉืœ ื”ืžื•ืžืก ื‘ื’ืจื/ืžื•ืœ
  6. ื”ืžื—ืฉื‘ื•ืŸ ืžื—ืฉื‘ ืื•ื˜ื•ืžื˜ื™ืช ื•ืžืฆื™ื’ ืืช ื”ืžื•ืœืœื™ื•ืช ื‘ืžื•ืœ/ืง"ื’

ื ื•ืกื—ืช ืžื•ืœืœื™ื•ืช ื•ื—ื™ืฉื•ื‘ื™ื

ื”ื ื•ืกื—ื” ื”ืžืชืžื˜ื™ืช

ื”ื‘ื™ื˜ื•ื™ ื”ืžืชืžื˜ื™ ืœืžื•ืœืœื™ื•ืช ื”ื•ื:

m=nsolutemsolvent=msolute/Msolutemsolventm = \frac{n_{solute}}{m_{solvent}} = \frac{m_{solute}/M_{solute}}{m_{solvent}}

ืื™ืคื”:

  • mm = ืžื•ืœืœื™ื•ืช (ืžื•ืœ/ืง"ื’)
  • nsoluten_{solute} = ืžืกืคืจ ื”ืžื•ืœื™ื ืฉืœ ื”ืžื•ืžืก
  • msolutem_{solute} = ืžืกืช ื”ืžื•ืžืก (ื’ืจื)
  • MsoluteM_{solute} = ืžืกืช ื”ืžื•ืœืœ ืฉืœ ื”ืžื•ืžืก (ื’ืจื/ืžื•ืœ)
  • msolventm_{solvent} = ืžืกืช ื”ืžืžืก (ืง"ื’)

ื”ืžืจื•ืช ื™ื—ื™ื“ื•ืช

ื‘ืขืช ืขื‘ื•ื“ื” ืขื ื™ื—ื™ื“ื•ืช ืฉื•ื ื•ืช, ื”ืžืจื•ืช ื”ื›ืจื—ื™ื•ืช:

  1. ื”ืžืจื•ืช ืžืกื”:

    • 1 ืง"ื’ = 1000 ื’ืจื
    • 1 ื’ืจื = 1000 ืž"ื’
    • 1 ืง"ื’ = 1,000,000 ืž"ื’
  2. ืœืžืกื” ืฉืœ ื”ืžื•ืžืก:

    • ืื ื‘ืง"ื’: ื”ื›ืคืœ ื‘-1000 ื›ื“ื™ ืœืงื‘ืœ ื’ืจืžื™ื
    • ืื ื‘ืž"ื’: ื—ืœืง ื‘-1000 ื›ื“ื™ ืœืงื‘ืœ ื’ืจืžื™ื
  3. ืœืžืกื” ืฉืœ ื”ืžืžืก:

    • ืื ื‘ื’ืจื: ื—ืœืง ื‘-1000 ื›ื“ื™ ืœืงื‘ืœ ืงื™ืœื•ื’ืจืžื™ื
    • ืื ื‘ืž"ื’: ื—ืœืง ื‘-1,000,000 ื›ื“ื™ ืœืงื‘ืœ ืงื™ืœื•ื’ืจืžื™ื

ื“ื•ื’ืžืื•ืช ื—ื™ืฉื•ื‘

ื“ื•ื’ืžื” 1: ื—ื™ืฉื•ื‘ ื‘ืกื™ืกื™

ื—ืฉื‘ ืืช ื”ืžื•ืœืœื™ื•ืช ืฉืœ ืคืชืจื•ืŸ ื”ืžื›ื™ืœ 10 ื’ืจื ืฉืœ NaCl (ืžืกืช ืžื•ืœืœ = 58.44 ื’ืจื/ืžื•ืœ) ื”ืžื•ืžืก ื‘-500 ื’ืจื ืžื™ื.

ืคืชืจื•ืŸ:

  1. ื”ืžืจืช ืžืกืช ื”ืžืžืก ืœืง"ื’: 500 ื’ืจื = 0.5 ืง"ื’
  2. ื—ื™ืฉื•ื‘ ืžื•ืœื™ื ืฉืœ ื”ืžื•ืžืก: 10 ื’ืจื รท 58.44 ื’ืจื/ืžื•ืœ = 0.1711 ืžื•ืœ
  3. ื—ื™ืฉื•ื‘ ืžื•ืœืœื™ื•ืช: 0.1711 ืžื•ืœ รท 0.5 ืง"ื’ = 0.3422 ืžื•ืœ/ืง"ื’

ื“ื•ื’ืžื” 2: ื™ื—ื™ื“ื•ืช ืฉื•ื ื•ืช

ื—ืฉื‘ ืืช ื”ืžื•ืœืœื™ื•ืช ืฉืœ ืคืชืจื•ืŸ ื”ืžื›ื™ืœ 25 ืž"ื’ ืฉืœ ื’ืœื•ืงื•ื– (Cโ‚†Hโ‚โ‚‚Oโ‚†, ืžืกืช ืžื•ืœืœ = 180.16 ื’ืจื/ืžื•ืœ) ื”ืžื•ืžืก ื‘-15 ื’ืจื ืžื™ื.

ืคืชืจื•ืŸ:

  1. ื”ืžืจืช ืžืกืช ื”ืžื•ืžืก ืœื’ืจื: 25 ืž"ื’ = 0.025 ื’ืจื
  2. ื”ืžืจืช ืžืกืช ื”ืžืžืก ืœืง"ื’: 15 ื’ืจื = 0.015 ืง"ื’
  3. ื—ื™ืฉื•ื‘ ืžื•ืœื™ื ืฉืœ ื”ืžื•ืžืก: 0.025 ื’ืจื รท 180.16 ื’ืจื/ืžื•ืœ = 0.0001387 ืžื•ืœ
  4. ื—ื™ืฉื•ื‘ ืžื•ืœืœื™ื•ืช: 0.0001387 ืžื•ืœ รท 0.015 ืง"ื’ = 0.00925 ืžื•ืœ/ืง"ื’

ื“ื•ื’ืžื” 3: ืจื™ื›ื•ื– ื’ื‘ื•ื”

ื—ืฉื‘ ืืช ื”ืžื•ืœืœื™ื•ืช ืฉืœ ืคืชืจื•ืŸ ื”ืžื›ื™ืœ 100 ื’ืจื ืฉืœ KOH (ืžืกืช ืžื•ืœืœ = 56.11 ื’ืจื/ืžื•ืœ) ื”ืžื•ืžืก ื‘-250 ื’ืจื ืžื™ื.

ืคืชืจื•ืŸ:

  1. ื”ืžืจืช ืžืกืช ื”ืžืžืก ืœืง"ื’: 250 ื’ืจื = 0.25 ืง"ื’
  2. ื—ื™ืฉื•ื‘ ืžื•ืœื™ื ืฉืœ ื”ืžื•ืžืก: 100 ื’ืจื รท 56.11 ื’ืจื/ืžื•ืœ = 1.782 ืžื•ืœ
  3. ื—ื™ืฉื•ื‘ ืžื•ืœืœื™ื•ืช: 1.782 ืžื•ืœ รท 0.25 ืง"ื’ = 7.128 ืžื•ืœ/ืง"ื’

ืฉื™ืžื•ืฉื™ื ืœื—ื™ืฉื•ื‘ื™ ืžื•ืœืœื™ื•ืช

ื™ื™ืฉื•ืžื™ื ืžืขื‘ื“ืชื™ื™ื

  1. ื”ื›ื ืช ืคืชืจื•ื ื•ืช ืขื ืขืฆืžืื•ืช ื˜ืžืคืจื˜ื•ืจื”

    • ื›ืืฉืจ ืคืชืจื•ื ื•ืช ืฆืจื™ื›ื™ื ืœืฉืžืฉ ื‘ื˜ืžืคืจื˜ื•ืจื•ืช ืฉื•ื ื•ืช
    • ืขื‘ื•ืจ ืชื’ื•ื‘ื•ืช ืฉื‘ื”ืŸ ืฉืœื™ื˜ื” ื‘ื˜ืžืคืจื˜ื•ืจื” ื”ื™ื ืงืจื™ื˜ื™ืช
    • ื‘ืžื—ืงืจื™ื ืงืจื™ื•ืกืงื•ืคื™ื™ื ืฉื‘ื”ื ืคืชืจื•ื ื•ืช ืžืงื•ืจืจื™ื ืžืชื—ืช ืœื˜ืžืคืจื˜ื•ืจืช ื”ื—ื“ืจ
  2. ื›ื™ืžื™ื” ืื ืœื™ื˜ื™ืช

    • ื‘ื˜ื™ื˜ืจืฆื™ื•ืช ื”ื“ื•ืจืฉื•ืช ืžื“ื™ื“ื•ืช ืจื™ื›ื•ื– ืžื“ื•ื™ืงื•ืช
    • ืœืื—ื™ื“ื•ืช ืฉืœ ืจื™ืื’ื ื˜ื™ื
    • ื‘ื‘ืงืจืช ืื™ื›ื•ืช ืฉืœ ืžื•ืฆืจื™ื ื›ื™ืžื™ื™ื
  3. ืžื—ืงืจ ื•ืคื™ืชื•ื—

    • ื‘ืคื™ืชื•ื— ืคื•ืจืžื•ืœืฆื™ื•ืช ืคืจืžืฆื‘ื˜ื™ื•ืช
    • ืขื‘ื•ืจ ื™ื™ืฉื•ืžื™ ืžื“ืข ื—ื•ืžืจื™ื
    • ื‘ื›ื™ืžื™ื” ืฉืœ ืžื–ื•ืŸ ืขื‘ื•ืจ ืขืงื‘ื™ื•ืช ื‘ืคื™ืชื•ื— ืžื•ืฆืจื™ื

ื™ื™ืฉื•ืžื™ื ืชืขืฉื™ื™ืชื™ื™ื

  1. ืชืขืฉื™ื™ืช ื”ืคืืจืžื”

    • ื‘ื”ื›ื ืช ืชืจื•ืคื•ืช ื•ื‘ืงืจืช ืื™ื›ื•ืช
    • ืขื‘ื•ืจ ืคืชืจื•ื ื•ืช ืคืจื ื˜ืจืœื™ื™ื ืฉื‘ื”ื ืจื™ื›ื•ื–ื™ื ืžื“ื•ื™ืงื™ื ื”ื ืงืจื™ื˜ื™ื™ื
    • ื‘ื‘ื“ื™ืงื•ืช ื™ืฆื™ื‘ื•ืช ืฉืœ ืžื•ืฆืจื™ื ืชืจื•ืคืชื™ื™ื
  2. ื™ื™ืฆื•ืจ ื›ื™ืžื™

    • ืขื‘ื•ืจ ื‘ืงืจืช ืชื”ืœื™ื›ื™ื ื‘ื™ื™ืฆื•ืจ ื›ื™ืžื™
    • ื‘ื‘ืงืจืช ืื™ื›ื•ืช ืฉืœ ืžื•ืฆืจื™ื ื›ื™ืžื™ื™ื
    • ืœืื—ื™ื“ื•ืช ืฉืœ ืจื™ืื’ื ื˜ื™ื ืชืขืฉื™ื™ืชื™ื™ื
  3. ืชืขืฉื™ื™ืช ื”ืžื–ื•ืŸ ื•ื”ืžืฉืงืื•ืช

    • ื‘ื‘ืงืจืช ืื™ื›ื•ืช ืฉืœ ืžื•ืฆืจื™ื ืžื–ื•ื ื™ื™ื
    • ืขื‘ื•ืจ ืขืงื‘ื™ื•ืช ื‘ืคื™ืชื•ื— ื˜ืขืžื™ื
    • ื‘ื˜ื›ื ื™ืงื•ืช ืฉื™ืžื•ืจ ื”ื“ื•ืจืฉื•ืช ืจื™ื›ื•ื–ื™ื ืกืคืฆื™ืคื™ื™ื ืฉืœ ืžื•ืžืก

ื™ื™ืฉื•ืžื™ื ืืงื“ืžื™ื™ื ื•ืžื—ืงืจื™ื™ื

  1. ืžื—ืงืจ ื‘ื›ื™ืžื™ื” ืคื™ื–ื™ืงืœื™ืช

    • ื‘ื—ืงื™ืจื•ืช ืชื›ื•ื ื•ืช ืงื•ืœื™ื’ื˜ื™ื‘ื™ื•ืช (ืขืœื™ื™ืช ื ืงื•ื“ืช ืจืชื™ื—ื”, ื™ืจื™ื“ืช ื ืงื•ื“ืช ืงื™ืคืื•ืŸ)
    • ืขื‘ื•ืจ ื—ื™ืฉื•ื‘ื™ ืœื—ืฅ ืื•ืกืžื•ื˜ื™
    • ื‘ืžื—ืงืจื™ ืœื—ืฅ ืื“ื™ื
  2. ืžื—ืงืจ ื‘ื‘ื™ื•ื›ื™ืžื™ื”

    • ืœื”ื›ื ืช ื‘ื•ืคืจื™ื
    • ื‘ืžื—ืงืจื™ ืงื™ื ื˜ื™ืงื” ืฉืœ ืื ื–ื™ืžื™ื
    • ืขื‘ื•ืจ ืžื—ืงืจื™ ืงื™ืคื•ืœ ื•ื™ืฆื™ื‘ื•ืช ืฉืœ ื—ืœื‘ื•ื ื™ื
  3. ืžื“ืข ื”ืกื‘ื™ื‘ื”

    • ื‘ื ื™ืชื•ื— ืื™ื›ื•ืช ืžื™ื
    • ืขื‘ื•ืจ ืžื—ืงืจื™ ื›ื™ืžื™ื” ืฉืœ ืงืจืงืข
    • ื‘ืžืขืงื‘ ื•ื”ืขืจื›ื” ืฉืœ ื–ื™ื”ื•ื

ื—ืœื•ืคื•ืช ืœืžื•ืœืœื™ื•ืช

ื‘ืขื•ื“ ืฉืžื•ืœืœื™ื•ืช ื”ื™ื ื‘ืขืœืช ืขืจืš ืขื‘ื•ืจ ื™ื™ืฉื•ืžื™ื ืจื‘ื™ื, ื™ื—ื™ื“ื•ืช ืจื™ื›ื•ื– ืื—ืจื•ืช ืขืฉื•ื™ื•ืช ืœื”ื™ื•ืช ืžืชืื™ืžื•ืช ื™ื•ืชืจ ื‘ืžืฆื‘ื™ื ืžืกื•ื™ืžื™ื:

  1. ืžื•ืœืจื™ื•ืช (M): ืžื•ืœื™ื ืฉืœ ืžื•ืžืก ืœื›ืœ ืœื™ื˜ืจ ืคืชืจื•ืŸ

    • ื™ืชืจื•ื ื•ืช: ืงืฉื•ืจื” ื™ืฉื™ืจื•ืช ืœื ืคื—, ื ื•ื—ื” ืœื ื™ืชื•ื—ื™ ื ืคื—
    • ื—ืกืจื•ื ื•ืช: ืžืฉืชื ื” ืขื ื˜ืžืคืจื˜ื•ืจื” ื‘ืฉืœ ื”ืชืคืฉื˜ื•ืช/ื”ืชื›ื•ื•ืฆื•ืช ื ืคื—
    • ื”ื˜ื•ื‘ ื‘ื™ื•ืชืจ ืขื‘ื•ืจ: ืชื’ื•ื‘ื•ืช ื‘ื˜ืžืคืจื˜ื•ืจืช ื”ื—ื“ืจ, ื”ืœื™ื›ื™ื ืžืขื‘ื“ืชื™ื™ื ืกื˜ื ื“ืจื˜ื™ื™ื
  2. ืื—ื•ื– ืžืกื” (% w/w): ืžืกื” ืฉืœ ืžื•ืžืก ืœื›ืœ 100 ื™ื—ื™ื“ื•ืช ืฉืœ ืžืกื” ืคืชืจื•ืŸ

    • ื™ืชืจื•ื ื•ืช: ืงืœ ืœื”ื›ื ื”, ืื™ืŸ ืฆื•ืจืš ื‘ืžื™ื“ืข ืขืœ ืžืกืช ืžื•ืœืœ
    • ื—ืกืจื•ื ื•ืช: ืคื—ื•ืช ืžื“ื•ื™ืง ืœื—ื™ืฉื•ื‘ื™ื ืกื˜ื•ื™ื›ื™ื•ืžื˜ืจื™ื™ื
    • ื”ื˜ื•ื‘ ื‘ื™ื•ืชืจ ืขื‘ื•ืจ: ืชื”ืœื™ื›ื™ื ืชืขืฉื™ื™ืชื™ื™ื, ื”ื›ื ื•ืช ืคืฉื•ื˜ื•ืช
  3. ืฉื‘ืจ ืžื•ืœ (ฯ‡): ืžื•ืœื™ื ืฉืœ ืžื•ืžืก ื—ืœืงื™ ืกืš ื”ืžื•ืœื™ื ื‘ืคืชืจื•ืŸ

    • ื™ืชืจื•ื ื•ืช: ืฉื™ืžื•ืฉื™ ืขื‘ื•ืจ ืฉื•ื•ื™ ืžืฉืงืœ ืื“ื™ื-ื ื•ื–ืœ, ืขื•ืงื‘ ืื—ืจื™ ื—ื•ืง ืจืื•ืœื˜
    • ื—ืกืจื•ื ื•ืช: ื™ื•ืชืจ ืžื•ืจื›ื‘ ืœื—ื™ืฉื•ื‘ ืขื‘ื•ืจ ืžืขืจื›ื•ืช ืžืจื•ื‘ื•ืช ืจื›ื™ื‘ื™ื
    • ื”ื˜ื•ื‘ ื‘ื™ื•ืชืจ ืขื‘ื•ืจ: ื—ื™ืฉื•ื‘ื™ื ืชืจืžื•ื“ื™ื ืžื™ื™ื, ืžื—ืงืจื™ ืฉื•ื•ื™ ืžืฉืงืœ ืคืื–ื”
  4. ื ื•ืจืžืœื™ื•ืช (N): ื’ืจื ืฉื•ื•ื™ ืฉืœ ืžื•ืžืก ืœื›ืœ ืœื™ื˜ืจ ืคืชืจื•ืŸ

    • ื™ืชืจื•ื ื•ืช: ืœื•ืงื—ืช ื‘ื—ืฉื‘ื•ืŸ ืืช ื”ืงื™ื‘ื•ืœืช ื”ืจื™ืืงื˜ื™ื‘ื™ืช ื‘ืชื’ื•ื‘ื•ืช ื—ื•ืžืฆื”-ื‘ืกื™ืก ืื• ื—ืžืฆื•ืŸ-ื—ื™ื–ื•ืง
    • ื—ืกืจื•ื ื•ืช: ืชืœื•ื™ื” ื‘ืชื’ื•ื‘ื” ื”ืกืคืฆื™ืคื™ืช, ื™ื›ื•ืœื” ืœื”ื™ื•ืช ืœื ื‘ืจื•ืจื”
    • ื”ื˜ื•ื‘ ื‘ื™ื•ืชืจ ืขื‘ื•ืจ: ื˜ื™ื˜ืจืฆื™ื•ืช ื—ื•ืžืฆื”-ื‘ืกื™ืก, ืชื’ื•ื‘ื•ืช ื—ืžืฆื•ืŸ-ื—ื™ื–ื•ืง

ื”ื™ืกื˜ื•ืจื™ื” ื•ืคื™ืชื•ื— ืฉืœ ืžื•ืœืœื™ื•ืช

ื”ืžื•ืฉื’ ืžื•ืœืœื™ื•ืช ืฆืฅ ื‘ืกื•ืฃ ื”ืžืื” ื”-19 ื›ืืฉืจ ื›ื™ืžืื™ื ื—ื™ืคืฉื• ื“ืจื›ื™ื ืžื“ื•ื™ืงื•ืช ื™ื•ืชืจ ืœืชืืจ ืจื™ื›ื•ื–ื™ ืคืชืจื•ื ื•ืช. ื‘ืขื•ื“ ืฉืžื•ืœืจื™ื•ืช (ืžื•ืœื™ื ืœืœื™ื˜ืจ ืคืชืจื•ืŸ) ื›ื‘ืจ ื”ื™ื™ืชื” ื‘ืฉื™ืžื•ืฉ, ืžื“ืขื ื™ื ื–ื™ื”ื• ืืช ื”ืžื’ื‘ืœื•ืช ืฉืœื” ื›ืืฉืจ ืžื“ื•ื‘ืจ ื‘ืžื—ืงืจื™ื ื”ืชืœื•ื™ื™ื ื‘ื˜ืžืคืจื˜ื•ืจื”.

ืคื™ืชื•ื— ืžื•ืงื“ื

ื‘ืฉื ื•ืช ื”-80 ืฉืœ ื”ืžืื” ื”-19, ื™ืขืงื•ื‘ื•ืก ื”ื ืจื™ืงื•ืก ื•ืืŸ 'ื˜ ื”ื•ืฃ ื•ืคืจื ืกื•ืื”-ืžืจื™ ืจืื•ืœื˜ ืขืจื›ื• ืขื‘ื•ื“ื•ืช ื—ืœื•ืฆื™ื•ืช ืขืœ ืชื›ื•ื ื•ืช ืงื•ืœื™ื’ื˜ื™ื‘ื™ื•ืช ืฉืœ ืคืชืจื•ื ื•ืช. ื”ืžื—ืงืจ ืฉืœื”ื ืขืœ ื™ืจื™ื“ืช ื ืงื•ื“ืช ื”ืงื™ืคืื•ืŸ, ืขืœื™ื™ืช ื ืงื•ื“ืช ื”ืจืชื™ื—ื” ื•ืœื—ืฅ ืื•ืกืžื•ื˜ื™ ื“ืจืฉ ื™ื—ื™ื“ืช ืจื™ื›ื•ื– ืฉืชืฉืืจ ืงื‘ื•ืขื” ืœืœื ืงืฉืจ ืœืฉื™ื ื•ื™ื™ื ื‘ื˜ืžืคืจื˜ื•ืจื”. ื”ืฆื•ืจืš ื”ื–ื” ื”ื•ื‘ื™ืœ ืœืื™ืžื•ืฅ ื”ืคื•ืจืžืœื™ ืฉืœ ืžื•ืœืœื™ื•ืช ื›ื™ื—ื™ื“ืช ืจื™ื›ื•ื– ืกื˜ื ื“ืจื˜ื™ืช.

ืกื˜ื ื“ืจื˜ื™ื–ืฆื™ื”

ื‘ืชื—ื™ืœืช ื”ืžืื” ื”-20, ื”ืžื•ืœืœื™ื•ืช ื”ืคื›ื” ืœื™ื—ื™ื“ืช ืกื˜ื ื“ืจื˜ื™ืช ื‘ื›ื™ืžื™ื” ืคื™ื–ื™ืงืœื™ืช, ื‘ืžื™ื•ื—ื“ ืขื‘ื•ืจ ืžื—ืงืจื™ื ืชืจืžื•ื“ื™ื ืžื™ื™ื. ื”ืื™ื’ื•ื“ ื”ื‘ื™ื ืœืื•ืžื™ ืœื›ื™ืžื™ื” ื˜ื”ื•ืจื” ื•ื™ื™ืฉื•ืžื™ืช (IUPAC) ื”ื›ื™ืจ ื‘ืžื•ืœืœื™ื•ืช ื›ื™ื—ื™ื“ืช ืจื™ื›ื•ื– ืกื˜ื ื“ืจื˜ื™ืช, ื•ื”ื’ื“ื™ืจ ืื•ืชื” ื›ืžืกืคืจ ื”ืžื•ืœื™ื ืฉืœ ื”ืžื•ืžืก ืœื›ืœ ืงื™ืœื•ื’ืจื ืฉืœ ืžืžืก.

ืฉื™ืžื•ืฉ ืžื•ื“ืจื ื™

ื”ื™ื•ื, ื”ืžื•ืœืœื™ื•ืช ืžืžืฉื™ื›ื” ืœื”ื™ื•ืช ื™ื—ื™ื“ืช ืจื™ื›ื•ื– ื—ื™ื•ื ื™ืช ื‘ืชื—ื•ืžื™ื ืžื“ืขื™ื™ื ืฉื•ื ื™ื:

  • ื‘ื›ื™ืžื™ื” ืคื™ื–ื™ืงืœื™ืช ืœื—ืงืจ ืชื›ื•ื ื•ืช ืงื•ืœื™ื’ื˜ื™ื‘ื™ื•ืช
  • ื‘ืžื“ืขื™ ื”ืคืืจืžื” ืœืคื™ืชื•ื— ืคื•ืจืžื•ืœืฆื™ื•ืช
  • ื‘ื‘ื™ื•ื›ื™ืžื™ื” ืœื”ื›ื ืช ื‘ื•ืคืจื™ื ื•ืœื™ืžื•ื“ื™ ืื ื–ื™ืžื™ื
  • ื‘ืžื“ืข ื”ืกื‘ื™ื‘ื” ืœื”ืขืจื›ืช ืื™ื›ื•ืช ืžื™ื

ืคื™ืชื•ื— ื›ืœื™ื ื“ื™ื’ื™ื˜ืœื™ื™ื ื›ืžื• ืžื—ืฉื‘ื•ืŸ ื”ืžื•ืœืœื™ื•ืช ื”ืคืš ืืช ื”ื—ื™ืฉื•ื‘ื™ื ื”ืœืœื• ืœื ื’ื™ืฉื™ื ื™ื•ืชืจ ืœืกื˜ื•ื“ื ื˜ื™ื ื•ืœืžืงืฆื•ืขื ื™ื ื›ืื—ื“, ืžื” ืฉืžืงืœ ืขืœ ืขื‘ื•ื“ื” ืžื“ื•ื™ืงืช ื•ื™ืขื™ืœื” ื™ื•ืชืจ ื‘ืžื“ืข.

ื“ื•ื’ืžืื•ืช ืงื•ื“ ืœื—ื™ืฉื•ื‘ ืžื•ืœืœื™ื•ืช

ื”ื ื” ื“ื•ื’ืžืื•ืช ื›ื™ืฆื“ ืœื—ืฉื‘ ืžื•ืœืœื™ื•ืช ื‘ืฉืคื•ืช ืชื›ื ื•ืช ืฉื•ื ื•ืช:

1' ื ื•ืกื—ืช Excel ืœื—ื™ืฉื•ื‘ ืžื•ืœืœื™ื•ืช
2' ื”ื ื—ื”:
3' A1 = ืžืกื” ืฉืœ ื”ืžื•ืžืก (ื’ืจื)
4' B1 = ืžืกืช ื”ืžื•ืœืœ ืฉืœ ื”ืžื•ืžืก (ื’ืจื/ืžื•ืœ)
5' C1 = ืžืกื” ืฉืœ ื”ืžืžืก (ื’ืจื)
6=A1/B1/(C1/1000)
7

ืฉืืœื•ืช ื ืคื•ืฆื•ืช

ืžื” ื”ื”ื‘ื“ืœ ื‘ื™ืŸ ืžื•ืœืœื™ื•ืช ืœืžื•ืœืจื™ื•ืช?

ืžื•ืœืœื™ื•ืช (m) ื”ื™ื ืžืกืคืจ ื”ืžื•ืœื™ื ืฉืœ ื”ืžื•ืžืก ืœื›ืœ ืงื™ืœื•ื’ืจื ืžืžืก, ื‘ืขื•ื“ ืฉืžื•ืœืจื™ื•ืช (M) ื”ื™ื ืžืกืคืจ ื”ืžื•ืœื™ื ืฉืœ ื”ืžื•ืžืก ืœื›ืœ ืœื™ื˜ืจ ืคืชืจื•ืŸ. ื”ื”ื‘ื“ืœ ื”ืžืจื›ื–ื™ ื”ื•ื ืฉืžื•ืœืœื™ื•ืช ืžืฉืชืžืฉืช ื‘ืžืกืช ื”ืžืžืก ื‘ืœื‘ื“, ื‘ืขื•ื“ ืฉืžื•ืœืจื™ื•ืช ืžืฉืชืžืฉืช ื‘ื ืคื— ืฉืœ ื›ืœ ื”ืคืชืจื•ืŸ. ื”ืžื•ืœืœื™ื•ืช ื ืฉืืจืช ืงื‘ื•ืขื” ืขื ืฉื™ื ื•ื™ื™ื ื‘ื˜ืžืคืจื˜ื•ืจื” ื›ื™ ื”ืžืกื” ืœื ืžืฉืชื ื” ืขื ื˜ืžืคืจื˜ื•ืจื”, ื‘ืขื•ื“ ืฉืžื•ืœืจื™ื•ืช ืžืฉืชื ื” ืขื ื˜ืžืคืจื˜ื•ืจื” ื›ื™ ื”ื ืคื— ืžืฉืชื ื” ืขื ื˜ืžืคืจื˜ื•ืจื”.

ืžื“ื•ืข ืžื•ืœืœื™ื•ืช ืžื•ืขื“ืคืช ืขืœ ืคื ื™ ืžื•ืœืจื™ื•ืช ื‘ื ื™ืกื•ื™ื™ื ืžืกื•ื™ืžื™ื?

ืžื•ืœืœื™ื•ืช ืžื•ืขื“ืคืช ื‘ื ื™ืกื•ื™ื™ื ื”ืžืขื•ืจื‘ื™ื ืฉื™ื ื•ื™ื™ื ื‘ื˜ืžืคืจื˜ื•ืจื”, ื›ืžื• ืžื—ืงืจื™ื ืขืœ ื™ืจื™ื“ืช ื ืงื•ื“ืช ื”ืงื™ืคืื•ืŸ ืื• ืขืœื™ื™ืช ื ืงื•ื“ืช ื”ืจืชื™ื—ื”. ืžื›ื™ื•ื•ืŸ ืฉื”ืžื•ืœืœื™ื•ืช ืžื‘ื•ืกืกืช ืขืœ ืžืกื” ื•ืœื ืขืœ ื ืคื—, ื”ื™ื ื ืฉืืจืช ืงื‘ื•ืขื” ืœืœื ืงืฉืจ ืœืฉื™ื ื•ื™ื™ื ื‘ื˜ืžืคืจื˜ื•ืจื”. ื–ื” ื”ื•ืคืš ืื•ืชื” ืœื™ืงืจื” ื‘ืžื™ื•ื—ื“ ืœื—ื™ืฉื•ื‘ื™ื ืชืจืžื•ื“ื™ื ืžื™ื™ื ื•ืœืžื—ืงืจื™ื ืขืœ ืชื›ื•ื ื•ืช ืงื•ืœื™ื’ื˜ื™ื‘ื™ื•ืช ืฉื‘ื”ืŸ ื”ื˜ืžืคืจื˜ื•ืจื” ื”ื™ื ืžืฉืชื ื”.

ื›ื™ืฆื“ ืื ื™ ื™ื›ื•ืœ ืœื”ืžื™ืจ ื‘ื™ืŸ ืžื•ืœืœื™ื•ืช ืœืžื•ืœืจื™ื•ืช?

ื”ืžืจื” ื‘ื™ืŸ ืžื•ืœืœื™ื•ืช ืœืžื•ืœืจื™ื•ืช ื“ื•ืจืฉืช ื™ื“ื™ืขื” ืขืœ ื”ืฆืคื™ืคื•ืช ืฉืœ ื”ืคืชืจื•ืŸ ื•ืžืกืช ื”ืžื•ืœืœ ืฉืœ ื”ืžื•ืžืก. ื”ื”ืžืจื” ื”ืžืฉื•ื™ื›ืช ื”ื™ื:

Molarity=Molalityร—densitysolution1+(Molalityร—Msolute/1000)Molarity = \frac{Molality \times density_{solution}}{1 + (Molality \times M_{solute} / 1000)}

ืื™ืคื”:

  • ื”ืฆืคื™ืคื•ืช ื”ื™ื ื‘ื’ืจื/ืž"ืœ
  • Mโ‚soluteโ‚Ž ื”ื™ื ืžืกืช ื”ืžื•ืœืœ ืฉืœ ื”ืžื•ืžืก ื‘ื’ืจื/ืžื•ืœ

ืขื‘ื•ืจ ืคืชืจื•ื ื•ืช ืžื“ื•ืœืœื™ื, ืขืจื›ื™ ืžื•ืœืจื™ื•ืช ื•ืžื•ืœืœื™ื•ืช ื”ื ืœืจื•ื‘ ืžืื•ื“ ืงืจื•ื‘ื™ื ืžืกืคืจื™ืช.

ื”ืื ืžื•ืœืœื™ื•ืช ื™ื›ื•ืœื” ืœื”ื™ื•ืช ืฉืœื™ืœื™ืช ืื• ืืคืก?

ืžื•ืœืœื™ื•ืช ืœื ื™ื›ื•ืœื” ืœื”ื™ื•ืช ืฉืœื™ืœื™ืช ืžื›ื™ื•ื•ืŸ ืฉื”ื™ื ืžื™ื™ืฆื’ืช ื›ืžื•ืช ืคื™ื–ื™ืช (ืจื™ื›ื•ื–). ื”ื™ื ื™ื›ื•ืœื” ืœื”ื™ื•ืช ืืคืก ื›ืืฉืจ ืื™ืŸ ืžื•ืžืก ื ื•ื›ื— (ืžืžืก ื˜ื”ื•ืจ), ืื‘ืœ ื–ื” ืคืฉื•ื˜ ื™ื”ื™ื” ื”ืžืžืก ื”ื˜ื”ื•ืจ ื•ืœื ืคืชืจื•ืŸ. ื‘ื—ื™ืฉื•ื‘ื™ื ืžืขืฉื™ื™ื, ืื ื• ื‘ื“ืจืš ื›ืœืœ ืขื•ื‘ื“ื™ื ืขื ืขืจื›ื™ ืžื•ืœืœื™ื•ืช ื—ื™ื•ื‘ื™ื™ื ื•ืœื ืืคืกื™ื™ื.

ื›ื™ืฆื“ ืžื•ืœืœื™ื•ืช ืžืฉืคื™ืขื” ืขืœ ื™ืจื™ื“ืช ื ืงื•ื“ืช ื”ืงื™ืคืื•ืŸ?

ื™ืจื™ื“ืช ื ืงื•ื“ืช ื”ืงื™ืคืื•ืŸ (ฮ”Tf) ื”ื™ื ืคืจื•ืคื•ืจืฆื™ื•ื ืœื™ืช ื™ืฉื™ืจื•ืช ืœืžื•ืœืœื™ื•ืช ืฉืœ ื”ืคืชืจื•ืŸ ืœืคื™ ื”ื ื•ืกื—ื”:

ฮ”Tf=Kfร—mร—i\Delta T_f = K_f \times m \times i

ืื™ืคื”:

  • ฮ”Tf ื”ื™ื ื™ืจื™ื“ืช ื ืงื•ื“ืช ื”ืงื™ืคืื•ืŸ
  • Kf ื”ื™ื ื”ืงื‘ื•ืข ื”ืงืจื™ื•ืกืงื•ืคื™ (ืกืคืฆื™ืคื™ ืœืžืžืก)
  • m ื”ื™ื ื”ืžื•ืœืœื™ื•ืช ืฉืœ ื”ืคืชืจื•ืŸ
  • i ื”ื•ื ื’ื•ืจื ื•ืืŸ 'ื˜ ื”ื•ืฃ (ืžืกืคืจ ื”ื—ืœืงื™ืงื™ื ื”ื ื•ืฆืจื™ื ื›ืืฉืจ ื”ืžื•ืžืก ืžืชืžื•ืกืก)

ื”ืงืฉืจ ื”ื–ื” ืขื•ืฉื” ืืช ื”ืžื•ืœืœื™ื•ืช ืฉื™ืžื•ืฉื™ืช ื‘ืžื™ื•ื—ื“ ืขื‘ื•ืจ ืžื—ืงืจื™ื ืงืจื™ื•ืกืงื•ืคื™ื™ื.

ืžื”ื™ ื”ืžื•ืœืœื™ื•ืช ืฉืœ ืžื™ื ื˜ื”ื•ืจื™ื?

ืžื™ื ื˜ื”ื•ืจื™ื ืื™ื ื ื‘ืขืœื™ ืขืจืš ืžื•ืœืœื™ื•ืช ืžื›ื™ื•ื•ืŸ ืฉืžื•ืœืœื™ื•ืช ืžื•ื’ื“ืจืช ื›ืžืกืคืจ ื”ืžื•ืœื™ื ืฉืœ ื”ืžื•ืžืก ืœื›ืœ ืงื™ืœื•ื’ืจื ืžืžืก. ื‘ืžื™ื ื˜ื”ื•ืจื™ื, ืื™ืŸ ืžื•ืžืก, ื›ืš ืฉื”ืžื•ืฉื’ ืžื•ืœืœื™ื•ืช ืื™ื ื• ื—ืœ. ื ืืžืจ ืฉืžื™ื ื˜ื”ื•ืจื™ื ืื™ื ื ืคืชืจื•ืŸ ืืœื ื—ื•ืžืจ ื˜ื”ื•ืจ.

ื›ื™ืฆื“ ืžื•ืœืœื™ื•ืช ืงืฉื•ืจื” ืœืœื—ืฅ ืื•ืกืžื•ื˜ื™?

ื”ืœื—ืฅ ื”ืื•ืกืžื•ื˜ื™ (ฯ€) ืงืฉื•ืจ ืœืžื•ืœืœื™ื•ืช ื“ืจืš ืžืฉื•ื•ืืช ื•ืืŸ 'ื˜ ื”ื•ืฃ:

ฯ€=MRT\pi = MRT

ืื™ืคื” M ื”ื™ื ืžื•ืœืจื™ื•ืช, R ื”ื•ื ืงื‘ื•ืข ื”ื’ื–, ื•-T ื”ื™ื ื˜ืžืคืจื˜ื•ืจื”. ืขื‘ื•ืจ ืคืชืจื•ื ื•ืช ืžื“ื•ืœืœื™ื, ืžื•ืœืจื™ื•ืช ื”ื™ื ื‘ืขืจืš ืฉื•ื•ื” ืœืžื•ืœืœื™ื•ืช, ื›ืš ืฉื ื™ืชืŸ ืœื”ืฉืชืžืฉ ื‘ืžื•ืœืœื™ื•ืช ื‘ืžืฉื•ื•ืื” ื–ื• ืขื ื˜ืขื•ืช ืžื™ื ื™ืžืœื™ืช. ืขื‘ื•ืจ ืคืชืจื•ื ื•ืช ืžืจื•ื›ื–ื™ื ื™ื•ืชืจ, ื™ืฉ ืฆื•ืจืš ื‘ื”ืžืจื” ื‘ื™ืŸ ืžื•ืœืœื™ื•ืช ืœืžื•ืœืจื™ื•ืช.

ื”ืื ื™ืฉ ื’ื‘ื•ืœ ืžืงืกื™ืžืœื™ ืืคืฉืจื™ ืœืžื•ืœืœื™ื•ืช ืฉืœ ืคืชืจื•ืŸ?

ื›ืŸ, ื”ื’ื‘ื•ืœ ื”ืžืงืกื™ืžืœื™ ื”ืืคืฉืจื™ ืœืžื•ืœืœื™ื•ืช ืžื•ื’ื‘ืœ ืขืœ ื™ื“ื™ ื”ืžืกื™ืกื•ืช ืฉืœ ื”ืžื•ืžืก ื‘ืžืžืก. ื‘ืจื’ืข ืฉื”ืžืžืก ื”ื•ืคืš ืœืจื•ื•ื™ ื‘ืžื•ืžืก, ืœื ื ื™ืชืŸ ืœื”ืžื™ืก ื™ื•ืชืจ, ืžื” ืฉืžื’ื“ื™ืจ ื’ื‘ื•ืœ ืขืœื™ื•ืŸ ืœืžื•ืœืœื™ื•ืช. ื’ื‘ื•ืœ ื–ื” ืžืฉืชื ื” ื‘ืžื™ื“ื” ืจื‘ื” ื‘ื”ืชืื ืœื–ื•ื’ ื”ืžื•ืžืก-ืžืžืก ื”ืกืคืฆื™ืคื™ ื•ืœืชื ืื™ื ื›ืžื• ื˜ืžืคืจื˜ื•ืจื” ื•ืœื—ืฅ.

ืขื“ ื›ืžื” ืžื“ื•ื™ืง ืžื—ืฉื‘ื•ืŸ ื”ืžื•ืœืœื™ื•ืช ืขื‘ื•ืจ ืคืชืจื•ื ื•ืช ืœื ืื™ื“ื™ืืœื™ื™ื?

ืžื—ืฉื‘ื•ืŸ ื”ืžื•ืœืœื™ื•ืช ืžืกืคืง ืชื•ืฆืื•ืช ืžืชืžื˜ื™ื•ืช ืžื“ื•ื™ืงื•ืช ืขืœ ืกืžืš ื”ืงืœื˜ื™ื ืฉื ื™ืชื ื™ื. ืขื ื–ืืช, ืขื‘ื•ืจ ืคืชืจื•ื ื•ืช ืžืจื•ื›ื–ื™ื ืžืื•ื“ ืื• ืœื ืื™ื“ื™ืืœื™ื™ื, ื’ื•ืจืžื™ื ื ื•ืกืคื™ื ื›ืžื• ืื™ื ื˜ืจืืงืฆื™ื•ืช ื‘ื™ืŸ ืžื•ืžืก ืœืžืžืก ืขืฉื•ื™ื™ื ืœื”ืฉืคื™ืข ืขืœ ื”ื”ืชื ื”ื’ื•ืช ื‘ืคื•ืขืœ ืฉืœ ื”ืคืชืจื•ืŸ. ื‘ืžืงืจื™ื ื›ืืœื”, ื”ืžื•ืœืœื™ื•ืช ื”ืžื—ื•ืฉื‘ืช ืขื“ื™ื™ืŸ ื ื›ื•ื ื” ื›ืžื“ื“ ืจื™ื›ื•ื–, ืืš ืชื—ื–ื™ื•ืช ืœื’ื‘ื™ ืชื›ื•ื ื•ืช ื”ืžื‘ื•ืกืกื•ืช ืขืœ ื”ืชื ื”ื’ื•ืช ืคืชืจื•ืŸ ืื™ื“ื™ืืœื™ืช ืขืฉื•ื™ื•ืช ืœื“ืจื•ืฉ ื’ื•ืจืžื™ ืชื™ืงื•ืŸ.

ื”ืื ืื ื™ ื™ื›ื•ืœ ืœื”ืฉืชืžืฉ ื‘ืžื•ืœืœื™ื•ืช ืขื‘ื•ืจ ืชืขืจื•ื‘ื•ืช ืžืžืกื™ื?

ื›ืŸ, ื ื™ืชืŸ ืœื”ืฉืชืžืฉ ื‘ืžื•ืœืœื™ื•ืช ื’ื ืขื ืžืžืกื™ื ืžืขื•ืจื‘ื™ื, ืืš ื”ื”ื’ื“ืจื” ืฆืจื™ื›ื” ืœื”ื™ื•ืช ืžื™ื•ืฉืžืช ื‘ื–ื”ื™ืจื•ืช. ื‘ืžืงืจื™ื ื›ืืœื”, ืชื—ืฉื‘ ืืช ื”ืžื•ืœืœื™ื•ืช ื‘ื™ื—ืก ืœืกืš ื”ืžืกื” ืฉืœ ื›ืœ ื”ืžืžืกื™ื ื™ื—ื“. ืขื ื–ืืช, ืขื‘ื•ืจ ืขื‘ื•ื“ื” ืžื“ื•ื™ืงืช ืขื ืžืžืกื™ื ืžืขื•ืจื‘ื™ื, ื™ื—ื™ื“ื•ืช ืจื™ื›ื•ื– ืื—ืจื•ืช ื›ืžื• ืฉื‘ืจ ืžื•ืœ ืขืฉื•ื™ื•ืช ืœื”ื™ื•ืช ืžืชืื™ืžื•ืช ื™ื•ืชืจ.

ืžืงื•ืจื•ืช

  1. ืื˜ืงื™ื ืก, ืค. ื•ื•., & ื“ื” ืคืื•ืœื”, ื’. (2014). ื›ื™ืžื™ื” ืคื™ื–ื™ืงืœื™ืช ืฉืœ ืื˜ืงื™ื ืก (ืžื”ื“ื•ืจื” 10). ื”ื•ืฆืืช ืื•ืงืกืคื•ืจื“.

  2. ืฆ'ืื ื’, ืจ., & ื’ื•ืœื“ืกื‘ื™, ืง. ื. (2015). ื›ื™ืžื™ื” (ืžื”ื“ื•ืจื” 12). ื”ื•ืฆืืช ืžืงื’ืจื•-ื”ื™ืœ.

  3. ื”ืืจื™ืก, ื“. ืก. (2015). ืื ืœื™ื–ื” ื›ื™ืžื™ืช ื›ืžื•ืชื™ืช (ืžื”ื“ื•ืจื” 9). ื”ื•ืฆืืช ื•ื•. ื”. ืคืจื™ืžืŸ ื•ื—ื‘ืจื”.

  4. IUPAC. (2019). ืžื“ืจื™ืš ื”ืžื•ื ื—ื™ื ื”ื›ื™ืžื™ื™ื (ื”ืกืคืจ "ื”ื–ื”ื‘"). ื”ื•ืฆืืช ื‘ืœืงื•ื•ืœ.

  5. ืœื•ื™ืŸ, ื. ื . (2008). ื›ื™ืžื™ื” ืคื™ื–ื™ืงืœื™ืช (ืžื”ื“ื•ืจื” 6). ื”ื•ืฆืืช ืžืงื’ืจื•-ื”ื™ืœ.

  6. ืกื™ืœื‘ืจื‘ืจื’, ืž. ืก., & ืืžื˜ื™ืก, ืค. (2018). ื›ื™ืžื™ื”: ื”ื˜ื‘ืข ื”ืžื•ืœืงื•ืœืจื™ ืฉืœ ื—ื•ืžืจ ื•ืฉื™ื ื•ื™ (ืžื”ื“ื•ืจื” 8). ื”ื•ืฆืืช ืžืงื’ืจื•-ื”ื™ืœ.

  7. ื–ื•ืžื“ืืœ, ืก. ืก., & ื–ื•ืžื“ืืœ, ืก. ื. (2016). ื›ื™ืžื™ื” (ืžื”ื“ื•ืจื” 10). ื”ื•ืฆืืช ืงื ื’'ื™ื™ื’'.

  8. ื‘ืจืื•ืŸ, ื˜. ืœ., ืœืžืื™, ื”. ื., ื‘ืจืกื˜ืŸ, ื‘. ื., ืžืจืคื™, ืฆ. ื’., ื•ื•ื“ื•ื•ืจื“, ืค. ืž., & ืกื˜ื•ืœืฆืคื•ืก, ืž. ื•ื•. (2017). ื›ื™ืžื™ื”: ื”ืžื“ืข ื”ืžืจื›ื–ื™ (ืžื”ื“ื•ืจื” 14). ื”ื•ืฆืืช ืคื™ืจืกื•ืŸ.

ืกื™ื›ื•ื

ืžื—ืฉื‘ื•ืŸ ื”ืžื•ืœืœื™ื•ืช ืžืกืคืง ื“ืจืš ืžื”ื™ืจื” ื•ืžื“ื•ื™ืงืช ืœืงื‘ื•ืข ืืช ื”ืจื™ื›ื•ื– ืฉืœ ืคืชืจื•ื ื•ืช ื‘ืžื•ื ื—ื™ื ืฉืœ ืžื•ืœืœื™ื•ืช. ื‘ื™ืŸ ืื ืืชื” ืกื˜ื•ื“ื ื˜ ื”ืœื•ืžื“ ืขืœ ื›ื™ืžื™ื” ืฉืœ ืคืชืจื•ื ื•ืช, ื—ื•ืงืจ ื”ืžื‘ืฆืข ื ื™ืกื•ื™ื™ื, ืื• ืžืงืฆื•ืขืŸ ื”ืขื•ื‘ื“ ื‘ืžืขื‘ื“ื”, ื›ืœื™ ื–ื” ืžืคืฉื˜ ืืช ืชื”ืœื™ืš ื”ื—ื™ืฉื•ื‘ ื•ืขื•ื–ืจ ืœื”ื‘ื˜ื™ื— ื“ื™ื•ืง ื‘ืขื‘ื•ื“ืชืš.

ื”ื‘ื ืช ื”ืžื•ืœืœื™ื•ืช ื•ื™ื™ืฉื•ืžื™ื” ื—ื™ื•ื ื™ืช ืขื‘ื•ืจ ืžื’ื•ื•ืŸ ืชื—ื•ืžื™ื ื‘ื›ื™ืžื™ื”, ื‘ืžื™ื•ื—ื“ ืืœื• ื”ืžืขื•ืจื‘ื™ื ื‘ืชืจืžื•ื“ื™ื ืžื™ืงื”, ืชื›ื•ื ื•ืช ืงื•ืœื™ื’ื˜ื™ื‘ื™ื•ืช, ื•ืชื”ืœื™ื›ื™ื ืชืœื•ื™ื™ ื˜ืžืคืจื˜ื•ืจื”. ืขืœ ื™ื“ื™ ืฉื™ืžื•ืฉ ื‘ืžื—ืฉื‘ื•ืŸ ื–ื”, ืชื•ื›ืœ ืœื—ืกื•ืš ื–ืžืŸ ื‘ื—ื™ืฉื•ื‘ื™ื ื™ื“ื ื™ื™ื ืชื•ืš ื›ื“ื™ ืจื›ื™ืฉืช ื”ื‘ื ื” ืขืžื•ืงื” ื™ื•ืชืจ ืฉืœ ื”ืงืฉืจื™ื ื‘ืจื™ื›ื•ื–ื™ื ื‘ื›ื™ืžื™ื” ืฉืœ ืคืชืจื•ื ื•ืช.

ื ืกื” ืืช ืžื—ืฉื‘ื•ืŸ ื”ืžื•ืœืœื™ื•ืช ืฉืœื ื• ืขื•ื“ ื”ื™ื•ื ื›ื“ื™ ืœื™ื™ืขืœ ืืช ืชื”ืœื™ืš ื”ื›ื ืช ื”ืคืชืจื•ื ื•ืช ืฉืœืš ื•ืœืฉืคืจ ืืช ื”ื“ื™ื•ืง ืฉืœ ืžื“ื™ื“ื•ืช ื”ืจื™ื›ื•ื– ืฉืœืš!

๐Ÿ”—

ื›ืœื™ื ืงืฉื•ืจื™ื

ื’ืœื” ืขื•ื“ ื›ืœื™ื ืฉืขืฉื•ื™ื™ื ืœื”ื™ื•ืช ืฉื™ืžื•ืฉื™ื™ื ืขื‘ื•ืจ ื–ืจื™ืžืช ื”ืขื‘ื•ื“ื” ืฉืœืš

ืžื—ืฉื‘ื•ืŸ ืžื•ืœืจื™ื•ืช: ื›ืœื™ ืœืจื™ื›ื•ื– ืคืชืจื•ื ื•ืช

ื ืกื” ืืช ื”ื›ืœื™ ื”ื–ื”

ืžื—ืฉื‘ื•ืŸ ื˜ื™ื˜ืจืฆื™ื”: ืงื‘ืข ื‘ืžื“ื•ื™ืง ืืช ืจื™ื›ื•ื– ื”ืื ืœื™ื˜

ื ืกื” ืืช ื”ื›ืœื™ ื”ื–ื”

ืžื—ืฉื‘ื•ืŸ ืžืกื” ืžื•ืœืจื™ืช ืขื‘ื•ืจ ืชืจื›ื•ื‘ื•ืช ื•ืžื•ืœืงื•ืœื•ืช ื›ื™ืžื™ื•ืช

ื ืกื” ืืช ื”ื›ืœื™ ื”ื–ื”

ืžื—ืฉื‘ื•ืŸ ืืœื™ื’ืฆื™ื”: ืคื™ืชืจื• ื‘ืขื™ื•ืช ืชืขืจื•ื‘ื•ืช ื•ื™ื—ืกื™ื ื‘ืงืœื•ืช

ื ืกื” ืืช ื”ื›ืœื™ ื”ื–ื”

ืžื—ืฉื‘ ื›ื•ื— ื™ื•ื ื™ ืขื‘ื•ืจ ืคืชืจื•ื ื•ืช ื›ื™ืžื™ื™ื

ื ืกื” ืืช ื”ื›ืœื™ ื”ื–ื”

ืžื—ืฉื‘ื•ืŸ ืคื•ื˜ื ืฆื™ืืœ ืžื™ื: ื ื™ืชื•ื— ืคื•ื˜ื ืฆื™ืืœ ืžื•ืžืก ื•ืœื—ืฅ

ื ืกื” ืืช ื”ื›ืœื™ ื”ื–ื”

ืžื—ืฉื‘ื•ืŸ ืจื™ื›ื•ื– ืคืชืจื•ื ื•ืช ืœื™ื™ืฉื•ืžื™ ื›ื™ืžื™ื”

ื ืกื” ืืช ื”ื›ืœื™ ื”ื–ื”