To solve this problem, we can use the combined gas law, which relates the pressure, volume, and temperature of a gas:
(P1 x V1) / T1 = (P2 x V2) / T2
where P1, V1, and T1 are the initial pressure, volume, and temperature, and P2, V2, and T2 are the final pressure, volume, and temperature, respectively.
First, let's convert the initial temperature of 30°C to Kelvin:
T1 = 30°C + 273.15 = 303.15 K
We can now set up the equation with the initial conditions:
(760 mmHg x V1) / 303.15 K = (P2 x 2V1) / 353.15 K
where V1 is the initial volume of the gas.
Simplifying this equation by multiplying both sides by 303.15 K and dividing by 2V1, we get:
P2 = (760 mmHg x 303.15 K) / (353.15 K) = 653.75 mmHg
Therefore, the final pressure of the gas is 653.75 mmHg when the volume is doubled and the temperature is increased to 80°C.