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Answer :
To find the vapor pressure of a mixture, convert weight percentages to moles, calculate the mole fractions, use Raoult's law to determine partial vapor pressures, and sum them. The approximate vapor pressure of the mixture at 20 ℃ is 77 psig.
To calculate the vapor pressure of an aerosol mixture at 20 ℃ consisting of 35% w/w CFC 114 with a vapor pressure of 31 psig and 65% w/w CFC 12 with a vapor pressure of 94.5 psig, assuming ideal behavior, we can use Raoult's law, which states that the partial vapor pressure of each component of an ideal mixture is equal to the vapor pressure of the pure substance multiplied by its mole fraction in the mixture. To find the mole fraction, we need to convert the weight percentages to moles.
Step 1: Convert the weight percentages to moles using the molecular weights provided.
For CFC 114: (35 g CFC 114) / (170.9 g/mol) = 0.2047 moles
For CFC 12: (65 g CFC 12) / (120.9 g/mol) = 0.5375 moles
Total moles = 0.2047 moles + 0.5375 moles = 0.7422 moles
Step 2: Calculate the mole fractions for each component.
Mole fraction of CFC 114 = 0.2047 moles / 0.7422 moles = 0.2757
Mole fraction of CFC 12 = 0.5375 moles / 0.7422 moles = 0.7243
Step 3: Use Raoult's law to determine the partial vapor pressures.
Partial vapor pressure of CFC 114 = (0.2757) × (31 psig) = 8.5467 psig
Partial vapor pressure of CFC 12 = (0.7243) × (94.5 psig) = 68.44635 psig
Step 4: Add the partial vapor pressures to get the total vapor pressure of the mixture.
Total vapor pressure = 8.5467 psig + 68.44635 psig = 76.99305 psig
After rounding to the nearest whole number, the total vapor pressure of the mixture at 20 ℃ is approximately 77 psig.
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