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=KHχSolving for the mole fraction
(χ) of methane, we have:
‌1=0.4×103×χ‌χ=2.5×10−3Step 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 ‌)=‌=55.5molAssuming
n (methane) is significantly smaller than 55.5 mol, substituting into Equation 2 simplifies to:
2.5×10−3=‌Solving for
n, the moles of methane:
‌n=2.5×10−3×55.5‌n=1.38×10−1Thus, the number of moles of methane dissolved in 1 L of water is
1.38×10−1.