To find the partial pressure of the third gas, helium, we can use the provided equation for the total pressure of a gas mixture:
[tex]\[ P_{\text{total}} = P_{\text{Neon}} + P_{\text{Argon}} + P_{\text{Helium}} \][/tex]
We know the following values:
- The total pressure of the gas mixture, [tex]\( P_{\text{total}} \)[/tex], is 1.25 atm.
- The partial pressure of neon, [tex]\( P_{\text{Neon}} \)[/tex], is 0.68 atm.
- The partial pressure of argon, [tex]\( P_{\text{Argon}} \)[/tex], is 0.35 atm.
We need to find the partial pressure of helium, [tex]\( P_{\text{Helium}} \)[/tex]. Rearranging the equation to solve for [tex]\( P_{\text{Helium}} \)[/tex], we get:
[tex]\[ P_{\text{Helium}} = P_{\text{total}} - P_{\text{Neon}} - P_{\text{Argon}} \][/tex]
Substitute the known values into the equation:
[tex]\[ P_{\text{Helium}} = 1.25 \, \text{atm} - 0.68 \, \text{atm} - 0.35 \, \text{atm} \][/tex]
Perform the subtraction step-by-step:
[tex]\[ P_{\text{Helium}} = 1.25 \, \text{atm} - (0.68 \, \text{atm} + 0.35 \, \text{atm}) \][/tex]
[tex]\[ P_{\text{Helium}} = 1.25 \, \text{atm} - 1.03 \, \text{atm} \][/tex]
[tex]\[ P_{\text{Helium}} = 0.22 \, \text{atm} \][/tex]
Therefore, the partial pressure of helium is:
[tex]\[ 0.22 \, \text{atm} \][/tex]
So the correct answer is:
[tex]\[ 0.22 \, \text{atm} \][/tex]
