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Gwar [14]
2 years ago
8

a 5L container contains 3 moles of helium and 4 moles of hydrogen at a pressure of 9 atms maintaining a constant T and additiona

l 2 mol or hydrogen are added.... what is the new partial pressure of hydrogen gas in a container
Chemistry
1 answer:
Stells [14]2 years ago
6 0

Answer:

7.71 atm

Explanation:

Given the following data:

V = 5 L

n_{He} = 3 mol

n_{H_2} = 4 mol

p_1 = 9 atm

T = const

According to the ideal gas law, we know that the product between pressure and volume of a gas is equal to the product between moles, the ideal gas law constant and the absolute temperature:

pV = nRT

Since the temperature and the ideal gas constant are constants, as well as the fixed container volume of 5 L, we may rearrange the equation as:

\frac{p}{n}=\frac{RT}{V}=const

This means for two conditions, we'd obtain:

\frac{p_1}{n_1}=\frac{p_2}{n_2}

Given:

p_1 = 9 atm

n_1 = n_{initial total} = n_{He} + n_{H_2} = 3 mol + 4 mol = 7 mol

n_2 = n_{final total} = n_{He} + n_{H_2} = 3 mol + 4 mol + 2 mol = 9 mol

Solve for the final pressure:

p_2 = p_1\cdot \frac{n_2}{n_1}

Now, according to the Dalton's law of partial pressures, the partial pressure is equal to the total pressure multiplied by the mole fraction of a component:

p_{H_2}=\chi_{H_2}p_2

Knowing that:

p_2 = p_1\cdot \frac{n_2}{n_1}

And:

\chi_{H_2}=\frac{n_H_2}{n_2}

The equation becomes:

p_{H_2}=\chi_{H_2}p_2=p_1\cdot \frac{n_2}{n_1}\cdot \frac{n_H_2}{n_2}=p_1\cdot \frac{n_H_2}{n_1}

Substituting the variables:

p_{H_2}=9 atm\cdot \frac{4 mol + 2 mol}{7 mol}=7.71 atm

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