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].
