Question

Using the same sample of gas ( p1 = 625 torr , t1 = 2 ∘c ), we wish to change the pressure to 6250 torr with no accompanying change in volume or amount of gas. what temperature t2 , in celsius, is needed to reach this pressure?

A) 20∘C
B) 25∘C
C) 30∘C
D) 35 ∘ C

Answer 1

The new temperature after a pressure increase from 625 to 6250 torr, Amontons's/Gay-Lussac's law is applied, but the resulting temperature is unreasonably high, suggesting an error in the calculation or the temperature scale interpretation.

Step-by-step explanation:

To find the temperature needed to increase the pressure of a gas from 625 torr to 6250 torr without changing its volume or amount, we must use Amontons's/Gay-Lussac's law. This law states that for a given quantity of gas at constant volume, the pressure is directly proportional to the temperature in kelvins (K).

To solve the problem, we will first convert the initial temperature from Celsius to Kelvin using the relationship T(K) = T(°C) + 273.15. Therefore:

T1 (in K) = 2 + 273.15 = 275.15 K

Using the relationship P1/T1 = P2/T2, we can solve for T2 as follows:

(625 torr / 275.15 K) = (6250 torr / T2 (in K))

This simplifies to T2 (in K) = (6250 torr * 275.15 K) / 625 torr. Calculating this gives:

T2 (in K) = 2751.5 K

To convert T2 back to Celsius, subtract 273.15 from the Kelvin value:

T2 (in °C) = 2751.5 K - 273.15 = 2478.35 °C

This temperature is outside the range of possible answer choices, implying there may be an error in the calculation or the interpretation of the temperature scale. A review of the calculation is recommended to find the correct temperature in Celsius that corresponds with the given pressure increase.