1. Calculate the decrease in temperature when 6.00 L at 20.0 °C is compressed to 4.00 L.
2. A container containing 5.00 L of a gas is collected at 100 K and then allowed to expand to 20.0 L. What must the new temperature be in order to maintain the same pressure (as required by Charles' Law)?
1. is pressure constant?
2. Use the combined gas law
P1V1/T1=P2V2/T2
Bye
To solve both questions, we can use the ideal gas law equation, which combines Boyle's Law, Charles' Law, and Gay-Lussac's Law. The ideal gas law equation is:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, and R is the ideal gas constant (0.0821 L·atm/mol·K).
1. To calculate the decrease in temperature when 6.00 L at 20.0 °C is compressed to 4.00 L:
Step 1: Convert the given temperature from Celsius to Kelvin by adding 273.15.
T1 = 20.0 °C + 273.15 = 293.15 K
Step 2: Plug the values into the ideal gas law equation for initial conditions:
P1 * V1 = n * R * T1
Step 3: Since the number of moles (n) and the pressure (P1) are constant, we can rewrite the equation as:
V1/T1 = constant
Step 4: Calculate the constant using the initial conditions:
constant = V1/T1 = 6.00 L / 293.15 K
Step 5: Use the constant to calculate the final temperature (T2) when the volume changes to 4.00 L:
V2/T2 = constant
4.00 L / T2 = 6.00 L / 293.15 K
Step 6: Rearrange the equation and solve for T2:
T2 = (4.00 L * 293.15 K) / 6.00 L
T2 = 195.43 K
Therefore, the decrease in temperature is 293.15 K - 195.43 K = 97.72 K.
2. To find the new temperature when the same pressure is maintained as the gas expands to 20.0 L:
Step 1: Convert the given temperature from Kelvin to Celsius by subtracting 273.15.
T1 = 100 K - 273.15 = -173.15 °C
Step 2: Plug the values into the ideal gas law equation for initial conditions:
P1 * V1 = n * R * T1
Step 3: Since the number of moles (n) and the pressure (P1) are constant, we can rewrite the equation as:
V1/T1 = constant
Step 4: Calculate the constant using the initial conditions:
constant = V1/T1 = 5.00 L / -173.15 °C
Step 5: Use the constant to calculate the final temperature (T2) when the volume changes to 20.0 L:
V2/T2 = constant
20.0 L / T2 = 5.00 L / -173.15 °C
Step 6: Rearrange the equation and solve for T2:
T2 = (20.0 L * -173.15 °C) / 5.00 L
T2 = -693.76 °C
Therefore, the new temperature should be -693.76 °C to maintain the same pressure as required by Charles' Law.