Final answer:
According to the Combined Gas Law, which relates the pressure, volume, and temperature of a gas, the new volume of the oxygen when heated to 315°C and the pressure increased to 1245.0 mmHg is approximately 7.5 liters, which is an option (a).
Step-by-step explanation:
The question involves applying the Combined Gas Law, which relates the pressure, volume, and temperature of a gas. In mathematical terms, it is expressed as P1V1/T1 = P2V2/T2, where P1 and V1 are the initial pressure and volume; T1 is the initial temperature; and P2, V2, T2 are the final pressure, volume, and temperature, respectively. Let's apply this formula to find the new volume V2.
First, convert all temperatures to Kelvin by adding 273.15, and pressures to atmospheres (1 atm = 760 mmHg). Starting values are P1 = 1 atm (because STP is defined as 1 atm), V1 = 15.0 L, T1 = 273.15 K (0°C at STP). The final values are P2 = 1245.0 mmHg / 760 mmHg/atm, T2 = 315°C + 273.15 K.
Using the Combined Gas Law:
P1V1/T1 = P2V2/T2
Solving for V2 gives us:
V2 = (P1V1T2) / (P2T1)
After plugging in the values and calculating, we get that V2 is approximately 7.5 liters, which corresponds to option (a).