Calculate the vapor pressure of an aerosol mixture containing HFA 134a and HFA 227, given their gauge…

Question

Calculate the vapor pressure of an aerosol mixture containing HFA 134a and HFA 227, given their gauge pressures and mass percentages.

ScanSolve AI Tutor · Accepted Answer

To calculate the vapor pressure of the aerosol mixture, we will use Raoult's Law and Dalton's Law of Partial Pressures. First, we need to convert the given gauge pressures to absolute pressures, then determine the mole fractions of each component, calculate their partial pressures, and finally sum them up.

Convert the given gauge pressures ( $P_{sig}$ ) to absolute pressures ( $P_{abs}$ ).
The atmospheric pressure is given as $14.7 \text{ Psia}$ .
$P_{abs} = P_{sig} + 14.7 \text{ Psia}$
For HFA 134a:
$P_{134a, abs} = 62.4 \text{ Psig} + 14.7 \text{ Psia} = 77.1 \text{ Psia}$
For HFA 227:
$P_{227, abs} = 56.0 \text{ Psig} + 14.7 \text{ Psia} = 70.7 \text{ Psia}$
Calculate the moles of each component.
Assume a total mass of $100 \text{ g}$ for the mixture.
Mass of HFA 134a = $30\% \text{ of } 100 \text{ g} = 30 \text{ g}$
Mass of HFA 227 = $70\% \text{ of } 100 \text{ g} = 70 \text{ g}$
$n_{134a} = \frac{30 \text{ g}}{102 \text{ g/mol}} = 0.2941 \text{ mol}$ $n_{227} = \frac{70 \text{ g}}{170 \text{ g/mol}} = 0.4118 \text{ mol}$
Calculate the total moles and mole fraction ( $X$ ) of each component.
$n_{total} = n_{134a} + n_{227} = 0.2941 \text{ mol} + 0.4118 \text{ mol} = 0.7059 \text{ mol}$ $X_{134a} = \frac{n_{134a}}{n_{total}} = \frac{0.2941 \text{ mol}}{0.7059 \text{ mol}} = 0.4166$ $X_{227} = \frac{n_{227}}{n_{total}} = \frac{0.4118 \text{ mol}}{0.7059 \text{ mol}} = 0.5834$
Calculate the partial vapor pressure ( $P'$ ) of each component using Raoult's Law ( $P' = X \cdot P_{abs}$ ).
$P'_{134a} = X_{134a} \times P_{134a, abs} = 0.4166 \times 77.1 \text{ Psia} = 32.12 \text{ Psia}$ $P'_{227} = X_{227} \times P_{227, abs} = 0.5834 \times 70.7 \text{ Psia} = 41.25 \text{ Psia}$
Calculate the total absolute vapor pressure ( $P_{total, abs}$ ) of the mixture.
$P_{total, abs} = P'_{134a} + P'_{227} = 32.12 \text{ Psia} + 41.25 \text{ Psia} = 73.37 \text{ Psia}$
Convert the total absolute vapor pressure back to gauge pressure ( $P_{total, sig}$ ).
$P_{total, sig} = P_{total, abs} - 14.7 \text{ Psia} = 73.37 \text{ Psia} - 14.7 \text{ Psia} = 58.67 \text{ Psig}$
Rounding to one decimal place:
$P_{total, sig} = 58.7 \text{ Psig}$
The total vapor pressure of the aerosol mixture is $\text{58.7 Psig}$ .

Calculate the vapor pressure of an aerosol mixture containing HFA 134a and HFA 227, given their gauge pressures and mass percentages.

Answer

Step-by-step solution

Convert the given gauge pressures ( $P_{sig}$ ) to absolute pressures ( $P_{abs}$ ).

Calculate the moles of each component.

Calculate the total moles and mole fraction ( $X$ ) of each component.

Calculate the partial vapor pressure ( $P'$ ) of each component using Raoult's Law ( $P' = X \cdot P_{abs}$ ).

Calculate the total absolute vapor pressure ( $P_{total, abs}$ ) of the mixture.

Convert the total absolute vapor pressure back to gauge pressure ( $P_{total, sig}$ ).

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More Chemistry Questions

Calculate the vapor pressure of an aerosol mixture containing HFA 134a and HFA 227, given their gauge pressures and mass percentages.

Answer

Step-by-step solution

Convert the given gauge pressures (PsigP_{sig}Psig​) to absolute pressures (PabsP_{abs}Pabs​).

Calculate the moles of each component.

Calculate the total moles and mole fraction (XXX) of each component.

Calculate the partial vapor pressure (P′P'P′) of each component using Raoult's Law (P′=X⋅PabsP' = X \cdot P_{abs}P′=X⋅Pabs​).

Calculate the total absolute vapor pressure (Ptotal,absP_{total, abs}Ptotal,abs​) of the mixture.

Convert the total absolute vapor pressure back to gauge pressure (Ptotal,sigP_{total, sig}Ptotal,sig​).

Try one yourself

Still stuck on this one?

More Chemistry Questions

Convert the given gauge pressures ( $P_{sig}$ ) to absolute pressures ( $P_{abs}$ ).

Calculate the total moles and mole fraction ( $X$ ) of each component.

Calculate the partial vapor pressure ( $P'$ ) of each component using Raoult's Law ( $P' = X \cdot P_{abs}$ ).

Calculate the total absolute vapor pressure ( $P_{total, abs}$ ) of the mixture.

Convert the total absolute vapor pressure back to gauge pressure ( $P_{total, sig}$ ).