Henry’s law constant for CO2 in water is 1.67×108Pa at 298K. What is the quantity of CO2 in 500mL of soda water when packed under 2.5 atm CO2 pressure at 298K?

Video Solution

Detailed Step-by-Step Solution

We are given the Henry’s law constant for CO₂ in water and the pressure under which soda water is packed. We must calculate the quantity of CO₂ dissolved in 500 mL of soda water at 298 K.

Henry’s constant (K_H) = 1.67 × 10⁸ Pa
Pressure of CO₂ = 2.5 atm
Temperature = 298 K
Volume of soda water = 500 mL = 0.5 L

Step 1: Convert Pressure into Pascal

Since K_H is given in Pascal, pressure must also be in Pascal.

1 atm = 1.013 × 10⁵ Pa
2.5 atm = 2.5 × 1.013 × 10⁵
= 2.53 × 10⁵ Pa

Step 2: Apply Henry’s Law

Henry’s law:

P = K_H × X

Rearranging:

X = P / K_H

Substitute values:

X = (2.53 × 10⁵) / (1.67 × 10⁸)
X ≈ 1.51 × 10⁻³

So, mole fraction of CO₂ in solution:

X_CO₂ ≈ 1.51 × 10⁻³

Step 3: Calculate Moles of Water

Assume density of water ≈ 1 g/mL

Mass of 500 mL water ≈ 500 g
Moles of water = 500 / 18
≈ 27.78 mol

Step 4: Use Mole Fraction Formula

X = n_CO₂ / (n_CO₂ + n_water)

Since solubility is small:

X ≈ n_CO₂ / n_water

1.51 × 10⁻³ = n / 27.78

n = 1.51 × 10⁻³ × 27.78
n ≈ 0.0419 mol

Step 5: Convert Moles to Mass

Molar mass of CO₂ = 44 g/mol

Mass = 0.0419 × 44
Mass ≈ 1.84 g

Quantity of CO₂ dissolved ≈ 1.84 g in 500 mL soda water

Theory: Henry’s Law and 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.

P = K_H X

Where:

P = Partial pressure of gas
K_H = Henry’s constant
X = Mole fraction of gas

A higher pressure increases gas solubility. This principle is used in carbonated beverages.

When the bottle is opened, pressure decreases, solubility decreases, and CO₂ escapes as bubbles.

Frequently Asked Questions

Why is pressure converted into Pascal?

Because Henry’s constant is given in Pascal, units must match.

Why is mole fraction used?

Henry’s law is expressed in terms of mole fraction.

Why is approximation used?

Because solubility is small, so n_CO₂ << n_water.

Why does soda fizz when opened?

Pressure decreases, reducing solubility of CO₂.

What does high K_H mean?

Higher K_H means lower solubility.

Is Henry’s law temperature dependent?

Yes. Gas solubility decreases with increase in temperature.

Is this important for exams?

Yes. Henry’s law numericals are common in CBSE and JEE.

Study Doubt

Henry’s law constant for CO2 in water is 1.67×108Pa at 298K. What is the quantity of CO2 in 500mL of soda water when packed under 2.5 atm CO2 pressure at 298K?

Video Solution

Detailed Step-by-Step Solution

Step 1: Convert Pressure into Pascal

Step 2: Apply Henry’s Law

Step 3: Calculate Moles of Water

Step 4: Use Mole Fraction Formula

Step 5: Convert Moles to Mass

Theory: Henry’s Law and Gas Solubility

Frequently Asked Questions

Why is pressure converted into Pascal?

Why is mole fraction used?

Why is approximation used?

Why does soda fizz when opened?

What does high K_H mean?

Is Henry’s law temperature dependent?

Is this important for exams?

Like this:

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A given coin has a mass of 3.0 g. Calculate the nuclear energy that would be required to separate all the neutrons and protons from each other. For simplicity assume that the coin is entirely made of ⁶³₂₉Cu atoms (of mass 62.92960 u).

The fission properties of ²³⁹₉₄Pu are very similar to those of ²³⁵₉₂U. The average energy released per fission is 180 MeV. How much energy, in MeV, is released if all the atoms in 1 kg of pure ²³⁹₉₄Pu undergo fission?

How long can an electric lamp of 100 W be kept glowing by fusion of 2.0 kg of deuterium? Take the fusion reaction as: ²₁H + ²₁H → ³₂He + n + 3.27 MeV

From the relation R = R₀A^(1/3), where R₀ is a constant and A is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of A).

Henry’s law constant for CO2 in water is 1.67×108Pa at 298K. What is the quantity of CO2 in 500mL of soda water when packed under 2.5 atm CO2 pressure at 298K?

Video Solution

Detailed Step-by-Step Solution

Step 1: Convert Pressure into Pascal

Step 2: Apply Henry’s Law

Step 3: Calculate Moles of Water

Step 4: Use Mole Fraction Formula

Step 5: Convert Moles to Mass

Theory: Henry’s Law and Gas Solubility

Frequently Asked Questions

Why is pressure converted into Pascal?

Why is mole fraction used?

Why is approximation used?

Why does soda fizz when opened?

What does high KH mean?

Is Henry’s law temperature dependent?

Is this important for exams?

Share this:

Like this:

Trending

A given coin has a mass of 3.0 g. Calculate the nuclear energy that would be required to separate all the neutrons and protons from each other. For simplicity assume that the coin is entirely made of ⁶³₂₉Cu atoms (of mass 62.92960 u).

The fission properties of ²³⁹₉₄Pu are very similar to those of ²³⁵₉₂U. The average energy released per fission is 180 MeV. How much energy, in MeV, is released if all the atoms in 1 kg of pure ²³⁹₉₄Pu undergo fission?

How long can an electric lamp of 100 W be kept glowing by fusion of 2.0 kg of deuterium? Take the fusion reaction as: ²₁H + ²₁H → ³₂He + n + 3.27 MeV

From the relation R = R₀A^(1/3), where R₀ is a constant and A is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of A).

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