Question:

At constant temperature, a gas is at a pressure of 940.3 mm Hg. The pressure at which its volume decreases by 40% is mm Hg. (Nearest integer)

Updated On: Mar 20, 2025
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Solution and Explanation

Step 1: Write the given data

  • Initial pressure, \( P_{\text{initial}} = 940.3 \, \text{mm Hg} \).
  • Initial volume, \( V_{\text{initial}} = 100 \, \text{units} \) (assumed). 
  • Final volume, \( V_{\text{final}} = 100 - 40\% = 60 \, \text{units} \).
  • Final pressure, \( P_{\text{final}} = ? \).



Step 2: Apply Boyle's Law

Boyle's law states that:

\[ P_{\text{initial}} \cdot V_{\text{initial}} = P_{\text{final}} \cdot V_{\text{final}}. \] Substitute the given values: \[ 940.3 \times 100 = P_{\text{final}} \times 60. \] Solving for \( P_{\text{final}} \): \[ P_{\text{final}} = \frac{940.3 \times 100}{60} = 1567.16 \, \text{mm Hg}. \] 

Step 3: Round to the nearest integer \[ P_{\text{final}} = 1567 \, \text{mm Hg}. \] 

Final Answer:

The pressure at which the volume decreases by 40% is \( P_{\text{final}} = 1567 \, \text{mm Hg}. \)

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Concepts Used:

Gas Laws

The gas laws were developed at the end of the 18th century, when scientists began to realize that relationships between pressure, volume and temperature of a sample of gas could be obtained which would hold to approximation for all gases.

The five gas laws are:

  • Boyle’s Law, which provides a relationship between the pressure and the volume of a gas.
  • Charles’s Law, which provides a relationship between the volume occupied by a gas and the absolute temperature.
  • Gay-Lussac’s Law, which provides a relationship between the pressure exerted by a gas on the walls of its container and the absolute temperature associated with the gas.
  • Avogadro’s Law, which provides a relationship between the volume occupied by a gas and the amount of gaseous substance.
  • The Combined Gas Law (or the Ideal Gas Law), which can be obtained by combining the four laws listed above.