A mixture of three noble gases has a total pressure of 1.25 atm. The partial pressures of two of the gases are 0.68 atm and 0.35 atm, respectively.

What is the partial pressure of the third gas?

A. 0.22 atm
B. 0.33 atm
C. 1.03 atm
D. 2.28 atm



Answer :

Let's solve this problem step by step.

1. Understanding the Problem:
We are given a mixture of three noble gases in a container, and the total pressure exerted by the mixture is 1.25 atm. We are also given the partial pressures of two of the gases: 0.68 atm and 0.35 atm. We need to find the partial pressure of the third gas.

2. Setting Up the Equation:
According to Dalton's Law of Partial Pressures, the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases. Mathematically, this is expressed as:
[tex]\[ P_T = P_1 + P_2 + P_3 + \ldots + P_n \][/tex]
where [tex]\( P_T \)[/tex] is the total pressure, and [tex]\( P_1, P_2, P_3, \ldots, P_n \)[/tex] are the partial pressures of the gases in the mixture.

In this case:
[tex]\[ P_T = 1.25 \, \text{atm} \][/tex]
[tex]\[ P_1 = 0.68 \, \text{atm} \][/tex]
[tex]\[ P_2 = 0.35 \, \text{atm} \][/tex]
We need to find [tex]\( P_3 \)[/tex], which is the partial pressure of the third gas.

3. Rearranging the Equation:
We can rearrange the equation to solve for [tex]\( P_3 \)[/tex]:
[tex]\[ P_3 = P_T - (P_1 + P_2) \][/tex]

4. Substituting the Known Values:
Let’s substitute the given values into the equation:
[tex]\[ P_3 = 1.25 \, \text{atm} - (0.68 \, \text{atm} + 0.35 \, \text{atm}) \][/tex]

5. Performing the Calculation:
[tex]\[ P_3 = 1.25 \, \text{atm} - 1.03 \, \text{atm} = 0.22 \, \text{atm} \][/tex]

6. Conclusion:
The partial pressure of the third gas is [tex]\( 0.22 \, \text{atm} \)[/tex].

Therefore, the correct answer is [tex]\( \boxed{0.22 \, \text{atm}} \)[/tex].

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