A gas is currently at a temperature of 84º C at a volume of 10 liters. If the pressure is kept the same and the temperature is lowered to 72º C, what will the new volume be?

9.66 L

Explanation:

The following data were obtained from the question:

Initial temperature (T1) = 84 ºC

Initial volume (V1) = 10 L

Final temperature (T2) = 72 ºC

Final volume (V2) =..?

Next, we shall convert celsius temperature to Kelvin temperature. This can be obtained as follow:

T(K) = T(°C) + 273

Initial temperature (T1) = 84 ºC

Initial temperature (T1) = 84 ºC + 273 = 357 K

Final temperature (T2) = 72 ºC

Final temperature (T2) = 72 ºC + 273 = 345 K

Since the pressure is constant, it means the gas is obeying Charles' law. Thus, we shall determine the new volume of the gas as follow:

Initial temperature (T1) = 357 K

Initial volume (V1) = 10 L

Final temperature (T2) = 345 K

Final volume (V2) =..?

V1/T1 = V2/T2

10/357 = V2/345

Cross multiply

357 × V2 = 10 × 345

Divide both side by 357

V2 = (10 × 345) / 357

V2 = 9.66 L

Thus, the new volume of the gas is 9.66 L.