Ideal Gas Law Calculation: Volume of Gas at Different Pressure and Temperature
What is the volume of a gas sample when the pressure and temperature are changed?
A 50.4 mL sample of gas is collected at 20.0 °C and 732.5 mmHg pressure. What is the volume of the gas if the pressure is changed to 760.0 mmHg and temperature of 26.3°C?
Calculation of Gas Volume at New Pressure and Temperature
If the pressure is changed to 760.0 mmHg and temperature of 26.3°C, the volume is 51.192 mL per ideal gas law.
The ideal gas law is a fundamental principle in chemistry that describes the behavior of gases under varying conditions of pressure, volume, and temperature. When the pressure and temperature of a gas sample are changed, we can calculate the new volume using the ideal gas law equation.
First, let's note down the given values:
- The initial volume (V1) of the gas is 50.4 mL.
- The initial temperature (T1) is 20 °C.
- The initial pressure (P1) is 732.5 mmHg.
Now, for the final conditions:
- The final temperature (T2) is 26.3 °C.
- The final pressure (P2) is 760.0 mmHg.
The ideal gas law requires temperatures to be in Kelvin. We convert the initial and final temperatures to Kelvin:
- T1 (Kelvin) = 20 °C + 273.15 = 293.15 K
- T2 (Kelvin) = 26.3 °C + 273.15 = 299.45 K
Substitute these values into the ideal gas law equation:
V2 = V1 x P2 x T1 / (P1 x T2)Plugging in the values, we get:
V2 = 50.4 mL x 760.0 mmHg x 293.15 K / (732.5 mmHg x 299.45 K)After calculation, the final volume (V2) is approximately 51.192 mL. Therefore, the volume of the gas at the new pressure of 760.0 mmHg and temperature of 26.3°C is 51.192 mL.
Understanding and applying the ideal gas law is crucial in various scientific calculations involving gases. It helps us determine the relationship between pressure, volume, and temperature, providing valuable insights into the behavior of gases.