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## Homework Statement

A high-pressure gas cylinder contains 20 ℓ of toxic gas at a pressure of [tex]1.8 \times 10^7 Pa[/tex] 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

[tex]PV=nRT[/tex]

## The Attempt at a Solution

[tex]\frac{PV}{T}=nR[/tex]

[tex]\frac{P_iV_i}{T_i}= \frac{P_fV_f}{T_f}[/tex]

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

[tex]\frac{P_i}{T_i}=\frac{P_f}{T_f}[/tex]

[tex]\frac{(1.8 \times 10^7)}{24}= \frac{P_f}{78.5}[/tex]

[tex]P_f=\frac{(1.8 \times 10^7)}{24} 78.5= 58875000[/tex]

But the correct answer to this problem has to be

**11800000**. Where is my the mistake?