Calculation of Original Temperature of Argon Gas Using Charles's Law

What was the original temperature of the argon gas?

If the final temperature of the argon gas was -51 °C and its volume decreased from 355 mL to 251 mL, what was the original temperature in °C?

Answer:

The original temperature of the argon gas was approximately 41°C.

To find the original temperature of the argon gas, we can use Charles's Law. Charles's Law states that the volume of a gas is directly proportional to its temperature, assuming pressure is constant. The formula for Charles's Law is V1/T1 = V2/T2, where:
V1 = Initial volume
T1 = Initial temperature
V2 = Final volume
T2 = Final temperature

Given the data provided:
Initial volume (V1) = 355 mL
Final volume (V2) = 251 mL
Final temperature (T2) = -51 °C

First, we need to convert the final temperature from Celsius to Kelvin by adding 273:
T2 = -51 °C + 273 = 222 K

Next, we can plug in these values into the Charles's Law formula and solve for the original temperature (T1):
V1/T1 = V2/T2
T1 = (V1 * T2) / V2
T1 = (355 mL * 222 K) / 251 mL
T1 ≈ 314 K

Finally, we convert the temperature back to Celsius by subtracting 273:
Original temperature ≈ 314 K - 273 ≈ 41 °C

Therefore, the original temperature of the argon gas was approximately 41 °C.