Henry's Law Calculations: Study with Video Lessons, Practice Problems & Examples

Henry's law relates the solubility of a gas to its partial pressure, expressed as $s=k$_h⁢p_gas, where s is solubility in molarity, k_h is the Henry's law constant, and p_gas is the partial pressure. The two-point form of Henry's law allows for comparisons between two solubilities and pressures: $s$₁/p₁=s₂/p₂. Understanding these relationships is crucial for applications in chemistry and environmental science.

Henry's Law Calculations Concept 1

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 $k_h$, 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've discussed this before where concentration and molarity are synonymous with one another. Usually, professors will interchange them. You can say concentration or molarity may mean the same thing. With this idea of Henry's law constant comes Henry's law formula, where $S_{\text{gas}}$, which equals the solubility of a gas in molarity equals Henry's constant, which is $k_h$, 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 torrs 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 when you might see it in molarities over torrs 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 $P_{\text{gas}}$. $P_{\text{gas}}$ is the partial pressure of the gas in atmospheres. And again, units are always important. The units here for partial pressure in atmosphere are because we're using these units for Henry's law constant, molarity over atmospheres.

Henry's Law Calculations Example 1

Calculate the solubility of carbon dioxide gas, which is CO₂, when its Henry's law constant is 8.20×102 molarities per atmosphere at a pressure of 3.29 atmospheres. Alright. So we need to find 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 8.20×102 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 2.70×103 molar. So this would be the concentration of carbon dioxide for this particular example question.

Henry's Law Calculations Concept 2

So now we take a look at Henry's law, at least in terms of 2.4. We're going to say the 2.4 method 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 for solubility can be in molarity, or they can be in other units that are in mass per volume. So the 2.4 form of Henry's law formula is solubility 1initial pressureP1=solubility 2final pressureP2. We use this version when we're dealing with two solubilities or two pressures for any given gas.

Henry's Law Calculations Example 2

At a pressure of 2.88 atmospheres, the solubility of dichloromethane, which is CH₂Cl₂, is 0.384 milligrams per liter. If the solubility decreases to 0.225 milligrams per liter, what is the new pressure? Alright. So here they're giving us one pressure, but they're asking for a new pressure. Since this is the first pressure that's given, we refer to it as 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 refer to as 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. We say here that S₁/P₁ = S₂/P₂. We are then going to plug in the numbers that we know, so this is 0.384 divided by 2.88 equals solubility 0.225 milligrams per liter divided by P₂, which we don't know. We will cross multiply these. When we do that, what we're going to see is: 0.384 milligrams per liter times P₂ equals 0.648 milligrams liter^-1 atmospheres. Divide both sides now by 0.384 milligrams per liter. So, these units cancel out and we'll have P₂ equal to 1.69 atmospheres as the final answer.

Henry's Law Constant for nitrogen in water is 1.67 x 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 0ºC and 1.00 atm, as much as 0.84 g of O₂ can dissolve in 1.0 L of water. At 0ºC 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 x 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:

What is Henry's Law and how is it used to calculate gas solubility?

Henry's Law states that the solubility of a gas in a liquid is directly proportional to the partial pressure of that gas above the liquid. The formula is given by:

$s=k_h{p}_{\mathrm{gas}}$

where $s$ is the solubility in molarity (M), $k_h$ is the Henry's Law constant, and $p_{\mathrm{gas}}$ is the partial pressure of the gas. This relationship helps in determining how much gas will dissolve in a liquid under different pressures, which is crucial in fields like chemistry and environmental science.

How do you use the two-point form of Henry's Law?

The two-point form of Henry's Law is used to compare the solubility of a gas at two different pressures. The formula is:

$\frac{s_1}{p_1}=\frac{s_2}{p_2}$

where $s_1$ and $s_2$ are the solubilities at pressures $p_1$ and $p_2$, respectively. This form is useful when you need to determine how a change in pressure affects the solubility of a gas.

What units are used for Henry's Law constant?

Henry's Law constant, denoted as $k_h$, is typically expressed in units of molarity per pressure. The most common units are molarity per atmosphere (M/atm). However, it can also be expressed in molarity per torr (M/torr) or molarity per millimeter of mercury (M/mmHg). When performing calculations, it's important to ensure that the units of pressure match those used for the Henry's Law constant to maintain consistency.

How does temperature affect Henry's Law constant?

Temperature has a significant impact on Henry's Law constant. Generally, as temperature increases, the solubility of gases in liquids decreases, which means the Henry's Law constant also decreases. This is because higher temperatures provide more kinetic energy to gas molecules, making them less likely to dissolve in the liquid. Therefore, when performing calculations involving Henry's Law, it's crucial to consider the temperature at which the constant was determined.

Can Henry's Law be applied to all gases?

Henry's Law is most accurate for gases that do not react chemically with the solvent and are at low concentrations. It is particularly applicable to ideal gases. However, for gases that react with the solvent or are present at high concentrations, deviations from Henry's Law can occur. In such cases, other models or corrections may be needed to accurately describe the solubility behavior.