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Pressure and Volume Change of a Gas

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I need some help in answering a question regarding caculations of how a compressed gas becomes a liquid:
10,000 m3 of natural gas as methane is the starting point at 288 Kelvin

We are told that 2 things happen to the gas:

1) The 10000 m3 gas volume is compressed from 101 KPa to 6895 KPa

I know this is PV =nRT but how do I get n for the mols and what do you get for volume?

2) Then, more difficult for me to understand --- when the compressed volume of gas is then cooled to 116 Kelvin (so ~ -250 degrees F) ---- I know this is cryogenic but how would I understand and calculate what the volume of the resultant liquid gas now is?

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1. So you don't need the moles to find the new volume. ...

Solution Summary

The solution calculates the new volume of a gas when pressure and temperature is changed with step-by-step explanations will all formulas presented.