AP EAPCET 18 May 2024 Shift 1 Solved Paper

To determine the number of moles of methane dissolved in 1 L of water at 293 K with a partial pressure of 1 bar, we employ Henry's law and the concept of mole fraction.
Given:
Partial pressure of methane, p0=1 bar
Henry's constant for methane, KH=0.4K bar
Step 1: Apply Henry's Law
Henry's law can be expressed as:
p0=KHχ
Solving for the mole fraction (χ) of methane, we have:
‌1=0.4×103×χ
‌χ=2.5×10−3
Step 2: Calculate Mole Fraction
The mole fraction of methane (x) in the solution is given by:
x=‌

n(‌ methane ‌)

n(‌ methane ‌)+n(‌ water ‌)

With 1 L of water, the number of moles of water is:
n(‌ water ‌)=‌

1000g

18g∕mol

=55.5mol
Assuming n (methane) is significantly smaller than 55.5 mol, substituting into Equation 2 simplifies to:
2.5×10−3=‌

n

55.5

Solving for n, the moles of methane:
‌n=2.5×10−3×55.5
‌n=1.38×10−1
Thus, the number of moles of methane dissolved in 1 L of water is 1.38×10−1.