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if a syringe with a vol of 25.2 ml has a gas inside with 352 millimoles and 100 mmol of gas is pumped into it at the same pressure and temp, what will be the new volume of gas in the syringe

The Ideal Gas Law states that PV=nRT where P is pressure, V is volume, n is number of molecules, R is the gas constant and T is the temp.

As temp does not change and pressure does not change, we move the constants to one side: V/n=RT/P=constant.

We get V1/n1=V2/n2

n1=352 milimoles

n2=352+100=452 millimoles

V2=n2*V1/n1=452*25.2/352

=32.36mL