A sample of gas contains $6.25 \times 10^{-3} mol$ in a 500.0 mL flask at $265^{\circ} C$. What is the pressure of the gas in kilopascals?
Formula: $P V=n R T(R=8.31 L \cdot kPa / mol \cdot K )$
Which variables are given?
pressure
volume
temperature
moles
Answer (1)
Use the ideal gas law formula: P V = n RT .
Rearrange the formula to solve for pressure: P = V n RT .
Substitute the given values: P = 0.500 L ( 6.25 × 1 0 − 3 mol ) × ( 8.31 mol ⋅ K L ⋅ kPa ) × ( 538.15 K ) .
Calculate the pressure: P ≈ 55.90 kPa .
Explanation
Problem Analysis We are given the number of moles of gas, the volume of the flask, and the temperature of the gas. We are asked to find the pressure of the gas in kilopascals. We will use the ideal gas law to solve for the pressure.
Identify Given Values and Formula The ideal gas law is given by P V = n RT , where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. We are given n = 6.25 × 1 0 − 3 mol , V = 500.0 mL = 0.500 L , T = 26 5 ∘ C = 265 + 273.15 = 538.15 K , and R = 8.31 mol ⋅ K L ⋅ kPa . We want to find P .
Rearrange the Formula We can rearrange the ideal gas law to solve for P : P = V n RT
Substitute the Values Now, we substitute the given values into the formula: P = 0.500 L ( 6.25 × 1 0 − 3 mol ) × ( 8.31 mol ⋅ K L ⋅ kPa ) × ( 538.15 K )
Calculate the Pressure Calculating the pressure: P = 0.500 6.25 × 1 0 − 3 × 8.31 × 538.15 ≈ 55.90 kPa
State the Final Answer The pressure of the gas is approximately 55.90 kPa .
Examples
Understanding the pressure of gases is crucial in various real-world applications. For instance, in designing scuba diving tanks, engineers need to calculate the amount of gas that can be safely stored at a specific pressure and temperature. Similarly, in the food industry, modified atmosphere packaging (MAP) relies on controlling the gas composition and pressure inside packages to extend the shelf life of perishable goods. By applying the ideal gas law, we can accurately predict and manage gas behavior in these scenarios, ensuring safety and efficiency.
