Question

A gas has a volume of 450.0 mL. If the temperature is held constant, what volume would the gas occupy if the pressure were
a. doubled?
b. reduced to one-fourth of its original value?

Answer 1

a) Answer:

= 225 mL

Explanation:

Using Boyle's law of gases;

The volume of a fixed mass of a gas is inversely proportional to its pressure at constant temperature.

Therefore;

P1V1 = P2V2

in this case; let the initial pressure be P;

Therefore; V1 = 450 mL, P1 = P, V2 = ? and P2 = 2P

Thus;

V2 = P1V1/P2

     = (P×450)/ (2P)

     = 225 mL

Therefore, the new volume will be 225 mL

b) Answer;

=1800 mL

Explanation;

Let the initial pressure be P;

Therefore; V1 = 450 mL, P1 = P, V2 = ? and P2 = 1/4P

Thus;

V2 = P1V1/P2

     = (P×450)/(0.25P)

      = 1800 mL

Thus, when the pressure is reduced to one-fourth of its original, the new volume will be 1800 mL.

Answer 2

Given that the initial volume of the gas is 450 mL, the new volume of the gas obtained based on the given data are:

A. The new volume of the gas when the pressure is doubled is 225 mL

B. The new volume of the gas when the pressure is reduced to one-fourth of its original value is 1800 mL

A. How to determine the new volume

• Initial volume (V₁) = 450 mL
• Temperature = constant
• Initial pressure (P₁) = P
• New pressure (P₂) = 2P

• New volume (V₂) =?

P₁V₁ / T₁ = P₂V₂ / T₂

Since the temperature is constant, we have:

P₁V₁ = P₂V₂

P × 450 = 2P × V₂

Divide both side by 2P

V₂ = (P × 450) / 2P

V₂ = 450 / 2

V₂ = 225 mL

B. How to determine the new volume

• Initial volume (V₁) = 450 mL
• Temperature = constant
• Initial pressure (P₁) = P
• New pressure (P₂) = ¼P

• New volume (V₂) =?

P₁V₁ / T₁ = P₂V₂ / T₂

Since the temperature is constant, we have:

P₁V₁ = P₂V₂

P × 450 = ¼P × V₂

450P = PV₂ / 4

Cross multiply

450P × 4 = PV₂

Divide both side by P

V₂ = (450P × 4) / P

V₂ = 450 × 4

V₂ = 1800 mL

Learn more about gas laws:

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