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Chapter 13: Problem 35

The solubility of \(\mathrm{CO}_{2}\) in water at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) is \(0.034 \mathrm{~mol} / \mathrm{L}\). What is its solubility under atmospheric conditions? (The partial pressure of \(\mathrm{CO}_{2}\) in air is 0.0003 atm.) Assume that \(\mathrm{CO}_{2}\) obeys Henry's law.

Short Answer

Expert verified
The solubility of CO2 under atmospheric conditions is 0.0000102 mol/L.

Step by step solution

01

Understand Henry's Law

Henry's Law states that at a constant temperature, the amount of a given gas that dissolves in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid. Mathematically it can be expressed as: \[S = kP\] Where, \(S\) is the solubility of the gas, \(k\) is Henry's law constant, and \(P\) is the partial pressure of the gas.
02

Determine the Henry's law constant

First, we need to calculate the value of Henry's law constant using the given conditions. We know the solubility (\(S1\)) is 0.034 mol/L and the partial pressure (\(P1\)) is 1 atm. Using Henry's Law, we get: \[0.034 = k \cdot 1\] Hence, \(k\) = 0.034 mol/L.atm
03

Find the new solubility

Now we need to find out the solubility of \(CO_2\) under the new partial pressure conditions which is that of atmospheric pressure. Given, the partial pressure under atmospheric conditions (\(P2\)) is 0.0003 atm. Using Henry's Law again where \(S\) is the unknown solubility and \(k\) = 0.034 mol/L.atm, the formula will be: \[0.034 \cdot 0.0003 = S\]
04

Calculate the solubility

Calculate the solubility by multiplying the values: \[S = 0.034 \cdot 0.0003\] \[S = 0.0000102 mol/L\]

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