To find the total pressure of the mixture of xenon, helium, and argon in atmospheres (atm), follow these steps:
1. Convert the pressures from kPa to atm:
- The conversion factor between kilopascals (kPa) and atmospheres (atm) is [tex]\(1 \, \text{atm} = 101.325 \, \text{kPa}\)[/tex].
2. Convert the pressure of each gas to atm:
- For xenon:
[tex]\[
\text{Pressure of xenon in atm} = \frac{28.99 \, \text{kPa}}{101.325 \, \text{kPa/atm}} \approx 0.2861 \, \text{atm}
\][/tex]
- For helium:
[tex]\[
\text{Pressure of helium in atm} = \frac{174.0 \, \text{kPa}}{101.325 \, \text{kPa/atm}} \approx 1.7172 \, \text{atm}
\][/tex]
- For argon:
[tex]\[
\text{Pressure of argon in atm} = \frac{57.9 \, \text{kPa}}{101.325 \, \text{kPa/atm}} \approx 0.5714 \, \text{atm}
\][/tex]
3. Sum the pressures of the individual gases to find the total pressure in atm:
[tex]\[
\text{Total pressure in atm} = 0.2861 \, \text{atm} + 1.7172 \, \text{atm} + 0.5714 \, \text{atm} = 2.5747 \, \text{atm}
\][/tex]
4. Round the total pressure to 2 decimal places:
[tex]\[
\text{Total pressure in atm} \approx 2.57 \, \text{atm}
\][/tex]
Thus, the total pressure of the mixture in atmospheres is [tex]\( \boxed{2.57} \)[/tex].
