Answer:
For Part A: The partial pressure of Helium is 218 mmHg.
For Part B: The mass of helium gas is 0.504 g.
Explanation:
We are given:
[tex]p_{CO_2}=245mmHg\\p_Ar}=119mmHg\\p_{O_2}=163mmHg\\P=745mmHg[/tex]
To calculate the partial pressure of helium, we use the formula:
[tex]P=p_{CO_2}+p_{Ar}+p_{O_2}+p_{He}[/tex]
Putting values in above equation, we get:
[tex]745=245+119+163+p_{He}\\p_{He}=218mmHg[/tex]
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,
[tex]PV=\frac{m}{M}RT[/tex]
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 = [tex]62.3637\text{ L.mmHg }mol^{-1}K^{-1}[/tex]
T = Temperature of helium gas = 283 K
Putting values in above equation, we get:
[tex]218mmHg\times 10.2L=\frac{m}{4g/mol}\times 62.3637\text{ L.mmHg }mol^{-1}K^{-1}\times 283K\\\\m=0.504g[/tex]
Hence, the mass of helium gas is 0.504 g.
A gas mixture with a total pressure of 745 mmHg contains COâ‚‚ (245 mmHg), Ar (119 mmHg), Oâ‚‚ (163 mmHg) and He (218 mmHg). 0.504 g of helium occupy 10.2 L at 283 K and 218 mmHg.
A gas mixture with a total pressure of 745 mmHg contains each of the following gases at the indicated partial pressures: COâ‚‚, 245 mmHg; Ar, 119 mmHg; Oâ‚‚, 163 mmHg; He, unknown partial pressure.
The total pressure is equal to the sum of the partial pressures.
[tex]P = pCO_2 + pAr + pO_2 + pHe\\\\pHe = P - pCO_2 - pAr - pO_2 = 745 mmHg - 245 mmHg - 119 mmHg - 163 mmHg = 218 mmHg[/tex]
Helium occupies 10.2 L at 218 mmHg and 283 K. We can calculate the moles of helium using the ideal gas equation.
[tex]P \times V = n \times R \times T\\\\n = \frac{P \times V}{R \times T} = \frac{218mmHg \times 10.2 L}{(62.4mmHg/mol.K) \times 283K} = 0.126 mol[/tex]
Finally, we will convert 0.126 moles of helium to grams using its molar mass (4.00 g/mol).
[tex]0.126 mol \times \frac{4.00g}{mol} = 0.504 g[/tex]
A gas mixture with a total pressure of 745 mmHg contains COâ‚‚ (245 mmHg), Ar (119 mmHg), Oâ‚‚ (163 mmHg) and He (218 mmHg). 0.504 g of helium occupy 10.2 L at 283 K and 218 mmHg.
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