Given: 

V\(_1\) = 100 cm\(^3\)  T\(_1\) = 35\(^0\)C + 273 = 308K  P\(_1\) = 750 mmHg

V\(_2\) = ? T\(_2\) = 35\(^0\)C + 273 = 308K  P\(_2\) = 100 mmHg

According to Boyle's law, the volume of a given mass of gas is inversely proportional to pressure, provided temperature remains constant.

Since temperature remains unchanged, it means T\(_1\) = T\(_2\), invariably meaning that temperature remains constant.

So, applying Boyle's law, P\(_1\) V\(_1\) = P\(_2\)V\(_2\) ( At constant temperature)

 V\(_2\) = \(\frac{{P_1}{V_1}}{P_2}\)

 V\(_2\) = \(\frac{{750}\times{100}}{100}\)

 V\(_2\) = 750cm\(^3\)