This is using the Combined Gas Law, which is the following:
\(\frac{P_{1}V_{1} }{T_{1}} = \frac{P_{2}V_{2} }{T_{2}}\), or \(P_{1} V_{1} T_{2} = P_{2} V_{2} T_{1}\)
Since you are solving for \(V_{2}\), you can change the equation to be: \(V_{2}\) = \(\frac{P_{1} V_{1} T_{2}}{{P_2}{T_1}}\)
Your given values are as follows:
\(P_{1}\): 2.5atm
\(V_{1}\): 2.3L
\(T_{1}\): 150°C
\(P_{2}\): 5atm
\(T_{2}\): 300°C
This formula only works if temperature is given in terms of Kelvin, so you can convert 150°C and 300°C to Kelvin by adding 273. Doing this, you get the following values:
\(T_{1}\)=423K
\(T_{2}\)573K
You then plug in all of the values you are given to get:
\(V_{2}\) = \(\frac {(2.5atm)(2.3L)(423K)}{(5atm)(573K)}\)
Multiply/divide all of the values to get:
\(V_{2}\) = 0.85L rounded to the nearest hundredth
