# Ideal Gas Law

roam

## Homework Statement

A high-pressure gas cylinder contains 20 ℓ of toxic gas at a pressure of $$1.8 \times 10^7 Pa$$ and a temperature of 24 °C. Its valve cracks when the cylinder is dropped. The cylinder is cooled to dry ice temperature (–78.5 °C) to reduce the leak rate and pressure so that it can be safely repaired.
What is the final pressure in the tank, assuming a negligible amount of gas leaks while being cooled and that there is no phase change?

## Homework Equations

$$PV=nRT$$

## The Attempt at a Solution

$$\frac{PV}{T}=nR$$

$$\frac{P_iV_i}{T_i}= \frac{P_fV_f}{T_f}$$

Because the problem says "a negligible amount of gas leaks", then the initial and final volumes of the gas are assumed to be equal, I will cancel the volumes

$$\frac{P_i}{T_i}=\frac{P_f}{T_f}$$

$$\frac{(1.8 \times 10^7)}{24}= \frac{P_f}{78.5}$$

$$P_f=\frac{(1.8 \times 10^7)}{24} 78.5= 58875000$$

But the correct answer to this problem has to be 11800000. Where is my the mistake?