Henry's Law Calculations: Videos & Practice Problems

Henry's law describes the relationship between the solubility of a gas and its partial pressure. The law is expressed through the formula:

$S_{\mathrm{gas}}=k_H\cdot P_{\mathrm{gas}}$

where Sgas is the solubility in molarity, kH is Henry's law constant (molarity/pressure), and Pgas is the partial pressure of the gas. The constant varies with temperature and solvent. Units for pressure can be in atmospheres, torrs, or millimeters of mercury, but it's essential to maintain consistency in units. When comparing two sets of conditions, the formula:

$\frac{S_1}{P_1}=\frac{S_2}{P_2}$

is used, where S1 and S2 are the initial and final solubilities, and P1 and P2 are the initial and final pressures. This demonstrates how changes in pressure can affect gas solubility, with solubility being directly proportional to the gas's partial pressure.

Henry's Law Calculations

The concentration, also referred to as the solubility of a dissolved gas, can be determined from its Henry's law constant and partial pressure. Now when I say Henry's law constant, that's the variable KH, and it represents the solubility of a gas at a fixed temperature in a particular solvent in molarity, which remember uses the variable capital M. Also remember we discussed this before where concentration and molarity are synonymous with one another. Usually, professors will interchange them. We can say concentration or molarity, and they mean the same thing.

With this idea of Henry's law constant comes Henry's law formula, where Cgas, which equals the solubility of a gas in molarity, equals Henry's constant which is KH, and here it's in units of molarity over pressure. So our normal type of pressure is atmospheres. But remember there's a possibility of tours or millimeters of mercury as well. So always be on the lookout for the units that you'll see for Henry's law constant. Usually, you'll see it in molarities over atmospheres, but there can be times where you might see it in molarities over tours or molarities over millimeters of mercury.

If it makes you feel more comfortable, just convert those pressure units all to atmospheres and use this version of Henry's law constant. Now, and that's times Pgas. Pgas is the partial pressure of the gas in atmospheres, and again, units are always important. The units here for partial pressure are atmospheres because we're using these units for Henry's law constant, molarity over atmospheres.

CO2 Solubility Example

Calculate the solubility of carbon dioxide gas, which is CO₂ when its Henry loss constant is 8.20 * 10 to the two molarities per atmosphere at a pressure of 3.29 atmospheres. All right, so we need to find the solubility of our gas. So that's S gas, which is CO₂ equals Henry's constant times the pressure of that gas.

So we're going to plug in 8.20 * 10 to the two molarities over atmospheres times 3.29 atmospheres. Again, you see that units will cancel out. And what do we have at the end? Molarity. So this would come out to be 27 * 10 to the three molar.

So this would be the concentration of carbon dioxide for this particular example question.

Henry's Law Two-point Formula

So now we take a look at Henry's law, at least in terms of the 2.4. We're going to say the 2.4 Met. Henry's law formula illustrates how changes in pressure can affect gas solubility.

Now we're going to say this formula. This version is used when dealing with two pressures and with two solubilities for a given gas. Here we're going to say with this formula the units from solubility can be in molarity or they can be in other units that are in mass per volume.

So Henry's law formula. The two point form is S1P1 = S2P2. So again, we use this version when we're dealing with two solubilities or two pressures for any given gas.

Henry's Law Two-point Formula Example

At a pressure of 2.88 atmospheres, the solubility of dichloromethane, which is Chapter 2 CL₂, is 0.384 milligrams per liter. If the solubility decreases to, oh, 0.225 milligrams per liter, what is the new pressure? All right, so here they're giving US1 pressure, but they're asking for a new pressure. So since this is the first pressure that's given, this is P₁. And since this is the second pressure that's talked about, this is P₂ connected to P₁.

Is this solubility which we're going to say is S₁ and connected to the new pressure we need to find? Is this solubility, which we call S₂? So now we're just going to solve, so we're going to say here that

S 1 P 1 = S 2 P 2

So then we're going to plug in the numbers that we know. So this is

0.384 2.88 = 0.225 P 2

which we don't know you're going to cross.

Multiply these two and cross multiply these two. So when we do that, what we're going to see is we're going to have

0.384 × P 2 = 0.648

milligrams over liters times atmospheres, divide both sides now by

0.384

milligrams per liter so these units cancel out and we'll have

P 2 = 2

atmospheres.

O here 2 = 16 atmospheres as my final answer.

Henry's Law Constant for nitrogen in water is 1.67 × 10^-4 M • atm^–1. If a closed canister contains 0.103 M nitrogen, what would be its pressure in atm?

• A. 617 atm
• B. 1.72 × 10^–5 atm
• C. 1.62 × 10^–3 atm
• D. 778 atm

Answer: (A)

At 0°C and 1.00 atm, as much as 0.84 g of O₂ can dissolve in 1.0 L of water. At 0°C and 4.00 atm, how many grams of O₂ dissolve in 1.0 L of water?

• A. 0.105 g
• B. 3.36 g
• C. 6.72 g
• D. 4.68 g

Answer: (B)

The atmospheric pressure in a lab is calculated as 1.3 atm. If oxygen gas contributes 62% of this atmospheric pressure, determine its mass (in g) dissolved at room temperature in 25 L of water. The Henry's Law Constant for oxygen in water at this temperature is 5.3 × 10^–5 M/atm.

• A. 1.4 × 10^–3 g
• B. 6.9 × 10^–5 g
• C. 0.055 g
• D. 0.034 g

Answer: (D)

Here’s what students ask on this topic:

How do you calculate Henry's law constant?

Henry's Law constant can be calculated by determining the ratio of the concentration of a gas in a liquid to the partial pressure of the gas above the liquid when the system is at equilibrium. The formula to calculate Henry's Law constant (_kH) is:

$k_H=\frac{C}{P}$

where:

• C is the concentration of the gas in the liquid (usually expressed in mol/L or M),
• P is the partial pressure of the gas above the liquid (usually expressed in atmospheres, atm, or Pascals, Pa).

The units of Henry's Law constant will depend on the units used for concentration and pressure. It's important to maintain consistency in the units when applying the formula.

To experimentally determine _kH, you would measure the concentration of the gas in the liquid at a known partial pressure at a constant temperature. This is because Henry's Law constant is temperature-dependent and will change with varying temperatures.