Q.Henry's law constant for CO2 in water is 1.67×108 Pa at 298 K. Calculate the quantity of CO2 in 500 mL of soda water when packed under 2.5 atm CO2 pressure at 298 K.
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Henry's Law: The Physics of "Fizz"
Imagine you open a cold bottle of soda. You hear that familiar psshhht sound. Bubbles rush out. Now think: why were those bubbles inside the bottle in the first place? The liquid wasn't boiling. The answer is Henry's Law.
The Intuition: Gas Wants to Dissolve
Gases are just molecules flying around. When a gas touches a liquid, some of those molecules get "trapped" inside the liquid — they dissolve. But here's the key: the more you push on the gas, the more of it gets forced into the liquid.
Think of a crowded bus. If you push more people toward the door (higher pressure), more people get squeezed inside. If you let the pressure off (open the bottle), people rush out. That's exactly what happens with gas and liquid.
In the soda bottle, carbon dioxide gas is pumped in at high pressure. That pressure forces a huge amount of CO₂ to dissolve into the liquid. When you open the bottle, the pressure above the liquid drops to normal air pressure. Suddenly, the liquid can't hold all that CO₂ anymore — so it escapes as bubbles. That's the fizz.
The Precise Statement
Henry's Law says:
C=kH⋅P
Where:
- C = concentration of the dissolved gas in the liquid (usually mol/L or g/L)
- P = partial pressure of that gas above the liquid (usually atm or kPa)
- kH = Henry's law constant — a number that depends on the specific gas, the liquid, and the temperature
In words: At a constant temperature, the amount of gas that dissolves in a liquid is directly proportional to the partial pressure of that gas above the liquid.
What the Constant kH Tells You
kH is not universal. It's different for every gas-liquid pair. For example:
- CO₂ in water has a certain kH
- O₂ in water has a different kH (smaller — oxygen doesn't dissolve as easily)
Temperature matters too. Higher temperature means lower kH — gases become less soluble in hot liquids. That's why a warm soda goes flat faster than a cold one.
Henry's Law works only for dilute solutions and non-reacting gases. If the gas reacts chemically with the liquid (like HCl gas dissolving in water to form hydrochloric acid), Henry's Law does not apply — the concentration will be much higher than predicted.
Real-Life Examples
| Situation | What Henry's Law explains |
|---|---|
| Soda fizz | High pressure forces CO₂ in; releasing pressure lets it out |
Why this formula?
Henry's Law: Why the Formula Holds
Henry's Law describes the solubility of a gas in a liquid at a constant temperature. The key formula is:
P=kH⋅x
Where:
- P = partial pressure of the gas above the liquid
- x = mole fraction of the gas dissolved in the liquid
- kH = Henry's constant (depends on gas, liquid, and temperature)
Why This Linear Relationship Exists
1. Dynamic Equilibrium at the Interface
Imagine a gas above a liquid. At the molecular level:
- Gas molecules constantly strike the liquid surface and dissolve
- Dissolved molecules constantly escape back into the gas phase
At equilibrium, the rate of dissolution equals the rate of escape. This is a dynamic balance, not a static one.
2. The Driving Force for Dissolution
The rate at which gas molecules enter the liquid depends on:
- How many gas molecules hit the surface — this is proportional to the partial pressure P of the gas
- How easily they dissolve — this is captured by kH
So:
Ratedissolve∝P
3. The Driving Force for Escape
The rate at which dissolved molecules leave the liquid depends on:
- How many dissolved molecules are near the surface — this is proportional to the mole fraction x of the gas in the liquid
- How easily they escape — also captured by kH
So:
Rateescape∝x
4. Equating the Two Rates
At equilibrium:
Ratedissolve=Rateescape
Therefore:
P∝x
Introducing the proportionality constant kH:
P=kH⋅x
Why It's Linear (Not Exponential or Logarithmic)
The linearity arises because:
- No saturation effects at low concentrations — the molecules don't "crowd" each other
- Ideal behavior is assumed — gas molecules don't interact strongly with each other or with the solvent
- Temperature is constant — kH doesn't change …
The quantity of CO2 dissolved in water is governed by Henry's Law, which relates the partial pressure of a gas above a liquid to its mole fraction in the solution.
p=KHx
where p is the partial pressure of the gas, KH is Henry's law constant, and x is the mole fraction of the gas in the solution.
- First, convert the given CO2 pressure from atmospheres to Pascals: PCO2=2.5 atm×101325 Pa/atm=253312.5 Pa.
- Next, use Henry's Law to find the mole fraction of CO2 in the soda water: xCO2=KHPCO2=1.67×108 Pa253312.5 Pa≈1.5168×10−3.
- Assume the density of soda water is approximately 1 g/mL. The moles of water in 500 mL are: nH2O=18.015 g/mol500 mL×1 g/mL≈27.754 mol. …
This problem uses Henry's Law to relate the partial pressure of CO2 above soda water to its mole fraction dissolved in the water. We then convert this mole fraction to the mass of CO2 dissolved in 500 mL of water, finding it to be approximately 1.85 g.
Henry's Law describes the relationship between the partial pressure of a gas above a liquid and the concentration of that gas dissolved in the liquid. It's a fundamental concept for understanding how gases like CO2 dissolve in beverages like soda water. The higher the partial pressure of the gas, the more of it will dissolve in the liquid, up to a certain point.
The law is expressed as:
P=KH⋅x
Where:
P is the partial pressure of the gas above the solution.
KH is Henry's Law constant for the specific gas and solvent at a given temperature.
x is the mole fraction of the gas dissolved in the solution.
In soda water, CO2 gas is dissolved under pressure. When you open a bottle of soda, the pressure above the liquid decreases, causing the dissolved CO2 to come out of solution as bubbles, which is why it fizzes. This problem asks us to calculate the amount of CO2 dissolved when packed under a specific pressure.
Let's break down the calculation step-by-step:
-
Identify Given Values and Target:
We are given:
- Henry's Law constant for CO2 (KH) = 1.67×108 Pa
- Volume of soda water = 500 mL
- Partial pressure of CO2 (PCO2) = 2.5 atm
- Temperature = 298 K (This confirms the KH value is appropriate for the conditions, but isn't directly used in the calculation itself).
Our goal is to find the "quantity" of CO2, which typically means its mass in grams or moles.
-
Convert Units for Consistency:
Henry's Law constant (KH) is given in Pascals (Pa), but the pressure (PCO2) is in atmospheres (atm). To use the formula correctly, both pressure values must be in the same units. We'll convert atmospheres to Pascals.
We know that 1 atm=101325 Pa.
PCO2=2.5 atm×1 atm101325 Pa=253312.5 Pa
-
Apply Henry's Law to Find the Mole Fraction of CO2:
Now we can use Henry's Law to find the mole fraction (xCO2) of CO2 dissolved in the water.
PCO2=KH⋅xCO2
Rearranging for xCO2:
xCO2=KHPCO2
xCO2=1.67×108 Pa253312.5 Pa
xCO2≈0.00151684
This mole fraction is a dimensionless quantity, representing the ratio of moles of CO2 to the total moles in the solution.
-
Calculate Moles of Solvent (Water):
Soda water is primarily water. We can assume that the 500 mL volume refers to the volume of water.
The density of water is approximately 1 g/mL.
Mass of water = Volume × Density
Mass of water = 500 mL×1 g/mL=500 g
Next, we need the molar mass of water (H2O).
Molar mass of H2O=(2×1.008 g/mol for H)+(1×16.00 g/mol for O)=18.016 g/mol.
Moles of water (nH2O) = Molar mass of waterMass of water
nH2O=18.016 g/mol500 g≈27.753 mol
Watch outWe assume the density of soda water is approximately the same as pure water. This is a reasonable approximation because the amount of dissolved CO2 is very small, as we will see.
-
Relate Mole Fraction to Moles of CO2: …
Method: Henry’s Law Application (Mole–Mass Conversion)
Concept first:
Henry’s law states that at constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid.
Mathematically:
p=KH⋅x
where
- p = partial pressure of the gas (in Pa)
- KH = Henry’s law constant (in Pa)
- x = mole fraction of the gas in the solution
Steps
Step 1: Convert pressure to SI units
Given pressure = 2.5 atm.
We know 1 atm = 1.01325×105 Pa.
p=2.5×1.01325×105=2.533×105 Pa
Step 2: Apply Henry’s law to find mole fraction
x=KHp=1.67×1082.533×105
x=1.517×10−3
This means: in the solution, for every 1 mole of total particles, 1.517×10−3 moles are CO2.
Step 3: Relate mole fraction to actual moles
For dilute solutions (soda water is mostly water),
x=nCO2+nH2OnCO2≈nH2OnCO2
because nCO2≪nH2O.
Step 4: Find moles of water in 500 mL …
Common Mistakes & How to Avoid Them — Henry’s Law Problem
Mistake 1: Confusing Henry’s Law Constant Units
The error:
Students often plug in KH without checking if pressure units match. Here, KH=1.67×108 Pa, but the given pressure is 2.5 atm.
How to avoid:
Always convert all pressures to the same unit before using Henry’s Law.
-
Convert 2.5 atm to Pa:
1 atm=1.01325×105 Pa
P=2.5×1.01325×105=2.533×105 Pa
-
Then apply Henry’s Law:
P=KH⋅x
where x = mole fraction of CO2 in water.
Mistake 2: Using the Wrong Form of Henry’s Law
The error:
Some students use P=KH⋅C (concentration in mol/L) when the constant is given for mole fraction.
How to avoid:
Check the definition of KH in the problem. Here, KH is in Pa, which means it relates pressure to mole fraction (dimensionless).
- Correct formula: xCO2=KHP=1.67×1082.533×105=1.517×10−3
Mistake 3: Forgetting to Account for the Solvent (Water)
The error:
Students calculate moles of CO2 directly from mole fraction without considering the moles of water.
How to avoid:
Mole fraction is:
xCO2=nCO2+nH2OnCO2
-
For dilute solutions, nCO2≪nH2O, so:
xCO2≈nH2OnCO2
-
Calculate moles of water in 500 mL:
Mass of water = 500 g (since density ≈ 1 g/mL)
nH2O=18500=27.78 mol
-
Then:
nCO2=xCO2×nH2O=1.517×10−3×27.78=0.0421 mol
Mistake 4: Stopping at Moles Instead of Mass …
Showing the 12 most recent of 21 on this concept.
- CBSE 2026Set V11 markMCQQ.The percentage of helium filled in the tanks used by most scuba divers to dilute air in deep dives(a) 32.1(b) 11.7(c) 74.2(d) 56.2
›Reveal solutionSolution
The air in a deep-diving scuba tank is diluted with about 11.7% helium.
At the high pressures experienced in deep dives, the solubility of atmospheric gases in blood increases (Henry's law, p=KHx). Nitrogen in particular dissolves and, on rapid ascent, is released as bubbles causing the painful and dangerous condition known as bends. To minimise this, the air supplied to divers is diluted with the sparingly-soluble, chemically inert gas hel …
- CBSE 2026Set ANNUAL1 markQ.On increasing temperature, solubility of gases in liquids ______ (fill in the blank).
›Reveal solutionSolution
Dissolution of a gas in a liquid is an exothermic process, so by Le Chatelier's principle, raising the temperature shifts the equilibrium back towards the gas phase, lowering solubility.
…
- CBSE 2025Set 56/4/11 markMCQQ.The value of Henry's constant KH is : (A) greater for gases with higher solubility (B) greater for gases with lower solubility (C) constant for all gases (D) not related to the solubility of gases
›Reveal solutionSolution
Henry’s constant KH is inversely related to gas solubility — a higher KH means lower solubility. So the correct option is (B).
Why Henry’s Law works this way
Henry’s Law describes the relationship between the partial pressure of a gas above a liquid and its concentration in the liquid. The law is written as:
p=KH⋅x
where p is the partial pressure of the gas, x is its mole fraction in the solution, and KH is Henry’s constant.
The key intuition: KH is essentially a resistance to dissolution. A gas that dissolves easily (high solubility) will need only a small partial pressure to achieve a given concentration — so KH is small. Conversely, a gas that barely dissolves (low solubility) needs a large partial pressure to force even a tiny amount into solution — so KH is large.
p=KH⋅x⇒KH=xp
Step-by-step reasoning
- Interpret the equation For a fixed partial pressure p, the mole fraction x of the dissolved gas is x=p/KH. Since p is constant, x (which measures solubility) is inversely proportional to KH:
x∝KH1
-
Relate KH to solubility
- High solubility → large x → small KH
- Low solubility → small x → large KH
-
Check the options
- (A) says KH is greater for gases with higher solubility — this is the opposite of what we just found.
- (B) says KH is greater for gases with lower solubility — this matches the inverse relationship. …
- CBSE 2025Set 56/5/11 markMCQQ.Two statements are given — one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below. (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (C) Assertion (A) is true, but Reason (R) is false. (D) Assertion (A) is false, but Reason (R) is true. Assertion (A) : Henry's law constant (KH) decreases with increase in temperature. Reason (R) : As the temperature increases, solubility of gases in liquids decreases.
›Reveal solutionSolution
Henry’s law constant KH actually increases with temperature, not decreases — so Assertion (A) is false. The Reason (R) is true: gas solubility does fall as temperature rises. The correct choice is (D).
Why this question trips students up
The trap here is subtle. Most of us remember that “solubility of gases decreases with temperature” — that’s drilled into us from everyday life (a cold soda fizzes more than a warm one). So Reason (R) feels solid.
But the Assertion talks about Henry’s law constant KH, not solubility directly. The two are inversely related, and that inverse relationship flips the temperature dependence. Let’s walk through it carefully.
Step-by-step reasoning
1. Recall Henry’s law
Henry’s law states that at constant temperature, the partial pressure of a gas above a liquid is proportional to its mole fraction in the liquid:
p=KH⋅x
Here KH is the Henry’s law constant. A larger KH means that for the same partial pressure, the gas dissolves less (smaller x). So KH is a measure of resistance to dissolution — it’s the opposite of solubility.
p=KH⋅x⇒x=KHp
2. What happens to solubility when temperature rises?
Dissolving a gas in a liquid is generally exothermic (heat is released). Le Chatelier’s principle tells us that raising temperature shifts equilibrium to favour the endothermic direction — which is the gas coming out of solution. So solubility x decreases.
That makes Reason (R) true.
3. Now connect KH to temperature …
- CBSE 2025Set ANNUAL1 markQ.State Henry's law.
›Reveal solutionSolution
Henry's law states that at constant temperature, the solubility (mole fraction) of a gas in a liquid is directly proportional to the partial pressure of that gas above the liquid.
Statement: The partial pressure of a gas in the vapour phase (p) is directly proportional to the mole fraction of the gas (x) dissolved in the solution, at a given temperature:
p=KH⋅x
where KH is the Henry's law constant, which is specific to the gas-solvent pair and depends on temperature.
…
- CBSE 2025Set ANNUAL1 markMCQQ.Dissolution of a gas in liquid is a process(a) with increase in enthalpy(b) with no change in enthalpy(c) with decrease in enthalpy(d) for which enthalpy change cannot be predicted
›Reveal solutionSolution
Dissolving a gas in a liquid is an exothermic process, so it occurs with a decrease in enthalpy.
When a gas dissolves in a liquid, gas molecules that were freely moving and widely separated come close to the solvent molecules and get surrounded by them (solvation). New, relatively strong solute–solvent (gas–liquid) interactions form as the gas molecules are trapped between solvent molecules. Energy is released when these new attractive interactions form, exactly as heat is released when a gas condenses.
…
- CBSE 2025Set ANNUAL1 markMCQQ.The Kₕ values of Ar(g), CO2(g), HCHO(g) and CH4(g) are 40.39, 1.67, 1.83 × 10⁻⁵ and 0.413 respectively. The correct order of their solubility is...(a) HCHO < CH4 < CO2 < Ar(b) HCHO < CO2 < CH4 < Ar(c) Ar < CO2 < CH4 < HCHO(d) Ar < CH4 < CO2 < HCHO
›Reveal solutionSolution
Henry's law constant KH and gas solubility are inversely related — a HIGHER KH means LOWER solubility.
By Henry's law, p=KH⋅x, where x is the mole fraction of dissolved gas. For a fixed partial pressure p, a larger KH forces a smaller mole fraction x to dissolve — so solubility falls as KH rises. Given: KH(Ar) = 40.39, KH(CO2) = 1.67, KH(CH4) = 0.413, KH(HCHO) = 1.83×10⁻⁵. Ranking KH from highest to lowest: A …
- CBSE 2024Set B1 markQ.Fill in the blank: The solubility of gas in a liquid is determined by ______ law.
›Reveal solutionSolution
Henry's law states that at constant temperature, the partial pressure of a gas above a solution is directly proportional to the mole fraction of the gas dissolved in the liquid.
Henry's law: p=KH⋅x, where p is the partial pressure of the gas above the solution, x is the mole fraction of the dissolved gas in the liquid, and KH is the Henry's law constant (specific to the gas-solvent pair and temperature). A higher KH means lower solubility for a given pressure. T …
- CBSE 2024Set ANNUAL1 markQ.The mathematical form of Henry's Law is ______.
›Reveal solutionSolution
Henry's Law states that the partial pressure of a gas in the vapour phase is directly proportional to its mole fraction dissolved in the solution.
Mathematically, Henry's Law is written as: p = KH . x …
- CBSE 2024Set ANNUAL1 markMCQQ.The value of Henry's constant K_H :(a) Increases with increase in temperature(b) Decreases with increase in temperature(c) Remains constant(d) First increases, then decreases
›Reveal solutionSolution
Gas solubility falls as temperature rises, and since KH is inversely related to solubility, KH rises with temperature.
Henry's law states p=KH⋅x, where p is the partial pressure of the gas above the solution and x is its mole fraction dissolved. A larger KH means a smaller x dissolves at the same pressure, i.e. lower solubility.
…
- CBSE 2023Set 56/1/11 markMCQQ.Low concentration of oxygen in the blood and tissues of people living at high altitude is due to : (A) high atmospheric pressure (B) low temperature (C) low atmospheric pressure (D) both low temperature and high atmospheric pressure
›Reveal solutionSolution
Henry’s Law states that the solubility of a gas in a liquid is directly proportional to its partial pressure. At high altitude, low atmospheric pressure reduces the partial pressure of oxygen, lowering its concentration in blood and tissues. The correct answer is (C).
Why Henry’s Law is the key
The question is about oxygen concentration in blood — not about how much oxygen is in the air, but how much dissolves into the bloodstream. That’s governed by Henry’s Law, which describes the solubility of a gas in a liquid.
C=kH⋅P
where C is the concentration of dissolved gas, kH is Henry’s constant (depends on the gas and temperature), and P is the partial pressure of the gas above the liquid.
For oxygen in blood, kH is fixed at body temperature. So the concentration of dissolved oxygen depends only on the partial pressure of oxygen in the air you breathe.
Step-by-step reasoning
-
At sea level, atmospheric pressure is about 1 atm. Oxygen makes up ~21% of air, so its partial pressure is PO2≈0.21×1=0.21 atm. Henry’s Law then gives a normal dissolved oxygen concentration in blood.
-
At high altitude (e.g., 3000–5000 m), total atmospheric pressure drops significantly — to about 0.7 atm at 3000 m, and even lower higher up. The fraction of oxygen in air stays 21%, but the partial pressure becomes PO2≈0.21×0.7=0.147 atm.
-
Applying Henry’s Law: Since C=kH⋅PO2, a lower PO2 directly gives a lower C. That’s why people at high altitude have low oxygen concentration in blood and tissues — not because the air has less oxygen percentage, but because the lower total pressure reduces oxygen’s partial pressure.
-
Check the options:
- (A) High atmospheric pressure — Wrong. High pressure would increase oxygen solubility, not decrease it. …
-
- CBSE 2023Set 56/2/11 markMCQQ.Value of Henry's constant KH : (A) increases with decrease in temperature. (B) decreases with increase in temperature. (C) increases with increase in temperature. (D) remains constant.
›Reveal solutionSolution
Henry’s constant KH measures gas solubility in a liquid. Since solubility decreases when temperature rises, KH must increase with temperature. The correct option is (C).
Why Henry’s constant behaves this way
Henry’s law states that at a constant temperature, the partial pressure of a gas above a liquid is proportional to its mole fraction in the liquid:
p=KH⋅x
Here KH is the Henry’s law constant. A larger KH means that for the same mole fraction x, the gas exerts a higher partial pressure — which implies the gas is less soluble (it prefers to stay in the vapour phase). Conversely, a smaller KH means the gas dissolves more readily.
So KH is an inverse measure of solubility: high KH → low solubility; low KH → high solubility.
How temperature affects solubility — and therefore KH
-
Think about dissolving a gas. When a gas dissolves in a liquid, the process is generally exothermic (heat is released). This is because gas molecules must be surrounded by solvent molecules, and the new intermolecular attractions release energy.
-
Le Chatelier’s principle. For an exothermic dissolution, heat is a product:
Gas+solvent⇌solution+heat
Raising the temperature adds heat, which shifts the equilibrium backward — toward the undissolved gas. So solubility decreases as temperature rises.
- Connect to KH. Since KH is inversely related to solubility, a decrease in solubility means KH must increase. Every textbook example confirms this: for oxygen in water, KH roughly doubles when going from 0 °C to 40 °C. …
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