Question c8a2e

Nov 22, 2015

$\text{0.9 atm}$

Explanation:

The idea here is that you can use Dalton's law of partial pressures to help you find a relationship between the total pressure of gaseous mixture and the partial pressure of $\text{B}$.

Now, the mole percent of a gas that's part of a gaseous mixture is simply the mole fraction of that gas multiplied by $100$.

color(blue)("mole%" = chi xx 100)" ", where

$\chi$ - the mole fraction of the gas

This means that you can use the mole percent of gas $\text{A}$ to determine the mole fraction of this gas.

$\frac{\text{mole %" = chi x 100 implies chi = "mole %}}{100}$

Therefore, you have

${\chi}_{\text{A}} = \frac{10}{100} = 0.1$

Since the mixture only contains two gases, $\text{A}$ and $\text{B}$, it follows that their respective mole fractions must add up to give $1$.

${\chi}_{\text{A" + chi_"B}} = 1$

This means that the mole fraction of $\text{B}$ will be

${\chi}_{\text{B}} = 1 - 0.1 = 0.9$

Now, STP conditions are usually given as a pressure of $\text{1 atm}$ and a temperature of ${0}^{\circ} \text{C}$.

SIDE NOTE I say usually because the actual conditions for STP are a pressure of $\text{100 kPa}$ and a temperature of ${0}^{\circ} \text{C}$.

Dalton's law of partial pressures tells you that the partial pressure of each component of a gaseous mixture is proportional to that component's mole fraction.

The total pressure of the mixture can thus be written as

P_"total" = overbrace(chi_"A" xx P_"total")^(color(red)("partial pressure of A")) + overbrace(chi_"B" xx P_"total")^(color(blue)("partial pressure of B"))

This means that the partial pressure of $\text{B}$ will be equal to

${P}_{\text{B" = chi_"B" xx P_"total}}$

P_"B" = 0.9 * "1 atm" = color(green)("0.9 atm")#

You can read more on mole percent and mole fraction here:

http://socratic.org/questions/what-is-mole-percent