<u>Answer:</u>
<u>For Part A:</u> The partial pressure of Helium is 218 mmHg.
<u>For Part B:</u> The mass of helium gas is 0.504 g.
<u>Explanation:</u>
We are given:
![p_{CO_2}=245mmHg\\p_Ar}=119mmHg\\p_{O_2}=163mmHg\\P=745mmHg](https://tex.z-dn.net/?f=p_%7BCO_2%7D%3D245mmHg%5C%5Cp_Ar%7D%3D119mmHg%5C%5Cp_%7BO_2%7D%3D163mmHg%5C%5CP%3D745mmHg)
To calculate the partial pressure of helium, we use the formula:
![P=p_{CO_2}+p_{Ar}+p_{O_2}+p_{He}](https://tex.z-dn.net/?f=P%3Dp_%7BCO_2%7D%2Bp_%7BAr%7D%2Bp_%7BO_2%7D%2Bp_%7BHe%7D)
Putting values in above equation, we get:
![745=245+119+163+p_{He}\\p_{He}=218mmHg](https://tex.z-dn.net/?f=745%3D245%2B119%2B163%2Bp_%7BHe%7D%5C%5Cp_%7BHe%7D%3D218mmHg)
Hence, the partial pressure of Helium is 218 mmHg.
To calculate the mass of helium gas, we use the equation given by ideal gas:
PV = nRT
or,
![PV=\frac{m}{M}RT](https://tex.z-dn.net/?f=PV%3D%5Cfrac%7Bm%7D%7BM%7DRT)
where,
P = Pressure of helium gas = 218 mmHg
V = Volume of the helium gas = 10.2 L
m = Mass of helium gas = ? g
M = Molar mass of helium gas = 4 g/mol
R = Gas constant = ![62.3637\text{ L.mmHg }mol^{-1}K^{-1}](https://tex.z-dn.net/?f=62.3637%5Ctext%7B%20L.mmHg%20%7Dmol%5E%7B-1%7DK%5E%7B-1%7D)
T = Temperature of helium gas = 283 K
Putting values in above equation, we get:
![218mmHg\times 10.2L=\frac{m}{4g/mol}\times 62.3637\text{ L.mmHg }mol^{-1}K^{-1}\times 283K\\\\m=0.504g](https://tex.z-dn.net/?f=218mmHg%5Ctimes%2010.2L%3D%5Cfrac%7Bm%7D%7B4g%2Fmol%7D%5Ctimes%2062.3637%5Ctext%7B%20L.mmHg%20%7Dmol%5E%7B-1%7DK%5E%7B-1%7D%5Ctimes%20283K%5C%5C%5C%5Cm%3D0.504g)
Hence, the mass of helium gas is 0.504 g.