Question

A sample of krypton gas occupies a volume of 8.96L at 48.0 Celsius and 1.08atm. If it is desired to decrease the volume of the gas sample to 7.71 L while decreasing its pressure to 0.855atm, the temperature of the gas sample at the new volume and pressure must be:

a) 62.3 Celsius

b) 57.8 Celsius

c) 48.0 Celsius

d) 51.5 Celsius

Answer 1

Using the Combined Gas Law to find the new temperature when volume and pressure change for krypton gas, none of the provided answer choices match the calculated temperature of approximately -51.05 °C. This suggests a discrepancy in the problem's data or the listed options.

Step-by-step explanation:

To determine the temperature of krypton gas at a new volume and pressure, we can use the Combined Gas Law, which combines Charles's Law, Boyle's Law, and Gay-Lussac's Law. The law is formulated as (P1 * V1) / T1 = (P2 * V2) / T2, where P is pressure, V is volume, and T is temperature in kelvins.

First, convert the initial and final temperatures to kelvins by adding 273.15 to the Celsius values:

• Initial temperature (T1) = 48.0 °C + 273.15 = 321.15 K
• Final temperature (T2) = ? (We need to find this)

Now, we use the Combined Gas Law and solve for T2:

(1.08 atm * 8.96 L) / 321.15 K = (0.855 atm * 7.71 L) / T2

9.7248 atm·L / 321.15 K = 6.60555 atm·L / T2

T2 = (6.60555 atm·L * 321.15 K) / 9.7248 atm·L

T2 = 215872.8325 / 9.7248

T2 ≈ 222.1 K

To find the Celsius temperature, subtract 273.15 from the Kelvin temperature:

T2(Celsius) = 222.1 K - 273.15 ≈ -51.05 °C

However, this result does not appear among the options given, indicating there may be an error in the problem or the options provided. Based on the calculations using the Combined Gas Law, the correct answer does not match any of the listed answer choices.