The temperature of a 350.0 mL sample of gas increases from 27°C to 277 °C. What is the final volume of the sample of gas if the pressure and amount of gas in the container is kept constant?
Answer (2)
Using Charles's Law, we find that the final volume of the gas sample increases to approximately 641.0 mL after the temperature rises from 27°C to 277°C. This calculation is based on the proportional relationship between volume and temperature at constant pressure. The temperatures are converted from Celsius to Kelvin to apply Charles's Law correctly.
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To find the final volume of a gas sample when the temperature changes, we can use Charles's Law. This law states that the volume of a gas is directly proportional to its temperature when the pressure and the number of moles remain constant. The formula for Charles's Law is:
T 1 V 1 = T 2 V 2
Where:
V 1 is the initial volume of the gas.
T 1 is the initial temperature in Kelvin.
V 2 is the final volume of the gas.
T 2 is the final temperature in Kelvin.
First, we need to convert the temperatures from Celsius to Kelvin:
Initial Temperature: 27°C
T 1 = 27 + 273.15 = 300.15 K
Final Temperature: 277°C
T 2 = 277 + 273.15 = 550.15 K
Now, plug the values into Charles's Law:
300.15 350.0 mL = 550.15 V 2
We can solve for V 2 :
V 2 = 300.15 350.0 × 550.15
V 2 ≈ 641.39 mL
So, the final volume of the gas is approximately 641.39 mL.
