What is the pressure of 0.540 mol of an ideal gas at 35.5 L and 222 K? Use [tex]P V=n R T[/tex] and [tex]R-8314 \frac{L \cdot i P_3}{m \cdot L}[/tex]
Answer (2)
Use the Ideal Gas Law equation: P V = n RT .
Rearrange the equation to solve for pressure: P = V n RT .
Substitute the given values: P = 35.5 L ( 0.540 mol ) ( 8.314 m o l ⋅ K L ⋅ k P a ) ( 222 K ) .
Calculate the pressure: P ≈ 28.2 kPa .
28.2 kPa
Explanation
Understanding the Problem We are given the Ideal Gas Law equation 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 the following values:
n = 0.540 mol
V = 35.5 L
T = 222 K
R = 8.314 m o l ⋅ K L ⋅ k P a
We need to find the pressure P .
Rearranging the Equation We can rearrange the Ideal Gas Law equation to solve for P :
P = V n RT
Substituting the Values Now, we substitute the given values into the equation:
P = 35.5 L ( 0.540 mol ) ( 8.314 m o l ⋅ K L ⋅ k P a ) ( 222 K )
Calculating the Pressure Calculating the pressure:
P = 35.5 0.540 × 8.314 × 222 kPa
P = 35.5 996.16512 kPa
P ≈ 28.0756 kPa
Final Answer The calculated pressure is approximately 28.0756 kPa. Looking at the given options, the closest value is 28.2 kPa.
Examples
The Ideal Gas Law is used in various real-world applications, such as predicting the behavior of gases in engines, weather forecasting, and calculating the amount of gas in a container. For example, if you're designing a compressed air tank, you need to know how much pressure the tank will experience at a certain temperature and volume. By using the Ideal Gas Law, engineers can ensure the tank is safe and efficient. This law helps us understand and predict the behavior of gases under different conditions, which is crucial in many scientific and engineering fields.
The pressure of 0.540 mol of an ideal gas at 35.5 L and 222 K is approximately 28.2 kPa, calculated using the Ideal Gas Law. By rearranging the equation to solve for pressure and substituting the known values, we find the result. This demonstrates how gas behavior can be predicted under specified conditions.
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