To solve this problem, we can use the combined gas law, which relates the pressure, temperature, and volume of a gas:
(P1 × V1)/T1 = (P2 × V2)/T2
where P1, V1, and T1 represent the initial pressure, volume, and temperature of the gas, and P2, V2, and T2 represent the new pressure, volume, and temperature of the gas, respectively.
At STP (standard temperature and pressure), the initial conditions are:
P1 = 1 atm
V1 = 10 L
T1 = 273 K (0°C)
To convert the temperature to Kelvin, we add 273 to the Celsius temperature.
The final conditions are:
P2 = 1520 mmHg
T2 = 512°C + 273 = 785 K
We can now solve for V2:
(P1 × V1)/T1 = (P2 × V2)/T2
(1 atm × 10 L)/(273 K) = (1520 mmHg × V2)/(785 K)
V2 = (1 atm × 10 L × 785 K)/(273 K × 1520 mmHg)
V2 = 9.0 L (rounded to one decimal place)
Therefore, the new volume of the gas is 9.0 liters if 10 liters of oxygen at STP are heated to 512°C and the pressure is also increased to 1520 mmHg.