High School

A vessel contains 1 mol of gas A, 2 mol of gas B, and 5 mol of gas C. The total pressure is 448 kPa. What are the partial pressures of the individual gases?

A. 56 kPa, 112 kPa, 280 kPa
B. 112 kPa, 224 kPa, 112 kPa
C. 64 kPa, 128 kPa, 256 kPa
D. 448 kPa, 0 kPa, 0 kPa

Answer :

Final answer:

Partial pressures are 56 kPa, 112 kPa, 280 kPa, respectively, for gases A, B, and C, hence the correct option is a. 56 kPa, 112 kPa, 280 kPa.

Explanation:

To find the partial pressures of each gas, we can use Dalton's law of partial pressures, which states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the individual gases.

Given:

Gas A: 1 mol

Gas B: 2 mol

Gas C: 5 mol

Total pressure: 448 kPa

First, we need to find the mole fraction of each gas:

For gas A: [tex]\frac{1\, mol}{1\,mol+2\,mol+5\,mol} =\frac{1}{8}[/tex]

For gas B: [tex]\frac{2\, mol}{1\,mol+2\,mol+5\,mol} =\frac{2}{8}[/tex]

For gas C: [tex]\frac{5\, mol}{1\,mol+2\,mol+5\,mol} =\frac{5}{8}[/tex]

Now, we can find the partial pressure of each gas:

Partial pressure of gas A: [tex]\frac{1}{8} \times 448kPa=56kPa[/tex]

Partial pressure of gas B: [tex]\frac{1}{4} \times 448kPa=112kPa[/tex]

Partial pressure of gas C: [tex]\frac{5}{8} \times 448kPa=280kPa[/tex]

Therefore, the correct answer is a. 56 kPa, 112 kPa, 280 kPa.