Answer:
1. Yes
2. After 68.1 mins, pX < pY.
Explanation:
Assuming the total gas pressure is 1 atm, let the partial pressure of Y be y, partial pressure of X will be 0.25y + y = 1.25y
1.25y + y = 1atm
2.25y = 1 atm
y = 1 atm / 2.25 = 0.44 atm
Then partial pressure of X = 0.56 atm
The partial pressure of a gas in a mixture of gases is directly proportional to the mole fraction of the gas.
Therefore the mole fraction of X and Y is 0.56 and 0.44 respectively.
The partial pressures of X and Y becomes half of their original values at 1.25 h = 85 min and Y at 150 min respectively.
The partial pressure after some time can be calculated from the half-life equation :
m = m⁰ * 1/2ⁿ
Where m = the remaining mass, m⁰ = initial mass, and n is number of half-lives undergone.
Let partial pressures represent the mass, and n for X and Y be a and b respectively:
pX = 0.56/2ᵃ
pY = 0.44/2ᵇ
We then determine when Partial pressure of X, pX = Partial pressure of Y, pY
0.56/2ᵃ = 0.44/2ᵇ
2ᵃ/2ᵇ = 0.56/0.44
2ᵃ/2ᵇ = 1.27
2ᵃ⁻ᵇ = 2⁰°³⁴⁵
a - b = 0.345
Let this time be t, therefore,
For X; t = 85a and For Y: t = 150b
85a = 150b
then, a = 1.76b
1.76b - b = 0.345
0.760b = 0.345
b = 0.454 and,
a = 0.345 + 0.454 = 0.799
So, X goes through 0.779 half-lives while Y goes through 0.454 half-lives Then, the time for both X and Y to have the same amount is:
t = 150 * 0.454 = 68.1 min
After 68.1 mins, pX < pY.
