Alright class, let's solve this problem step-by-step using the information provided and the formula for the total pressure of a gas mixture, [tex]\( P_T = P_1 + P_2 + P_3 + \ldots + P_n \)[/tex].
Step 1: Identify the given values
We are given:
- The total pressure of the gas mixture, [tex]\( P_T \)[/tex], is 1.25 atm.
- The partial pressure of neon, [tex]\( P_{Ne} \)[/tex], is 0.68 atm.
- The partial pressure of argon, [tex]\( P_{Ar} \)[/tex], is 0.35 atm.
Step 2: Write down the formula
The formula for the total pressure of a mixture of gases is:
[tex]\[ P_T = P_{Ne} + P_{Ar} + P_{He} \][/tex]
Step 3: Substitute the known values into the formula
We know the total pressure and the partial pressures of neon and argon:
[tex]\[ 1.25 \text{ atm} = 0.68 \text{ atm} + 0.35 \text{ atm} + P_{He} \][/tex]
Step 4: Solve for the unknown, [tex]\( P_{He} \)[/tex]
First, add the partial pressures of neon and argon:
[tex]\[ 0.68 \text{ atm} + 0.35 \text{ atm} = 1.03 \text{ atm} \][/tex]
Next, subtract this sum from the total pressure to find the partial pressure of helium:
[tex]\[ P_{He} = 1.25 \text{ atm} - 1.03 \text{ atm} \][/tex]
Step 5: Perform the subtraction
[tex]\[ P_{He} = 0.22 \text{ atm} \][/tex]
So, the partial pressure of helium in the mixture is [tex]\( 0.22 \)[/tex] atm.
Thus, the correct answer from the given options is:
[tex]\[ \boxed{0.22 \text{ atm}} \][/tex]
