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 and T1 are the initial pressure and temperature, V1 is the initial volume, P2 is the final pressure (assumed to be constant in this problem), V2 is the final volume (what we want to find), and T2 is the final temperature.
We can rearrange this equation to solve for V2:
V2 = (P1 x V1 x T2)/(P2 x T1)
We are given that the initial volume (V1) is 4.45 L, the initial temperature (T1) is 35.0°C, and the final temperature (T2) is 75.0°C. We are also told that the pressure is constant, so we can assume that P1 = P2.
We need to convert the temperatures to Kelvin, since temperature must be in Kelvin for gas law calculations. To convert Celsius to Kelvin, we add 273.15:
T1 = 35.0°C + 273.15 = 308.15 K
T2 = 75.0°C + 273.15 = 348.15 K
Now we can substitute these values into the equation:
V2 = (P1 x V1 x T2)/(P2 x T1) = (1 x 4.45 x 348.15)/(1 x 308.15) = 5.02 L
Therefore, the new volume is 5.02 L when the temperature is increased to 75.0°C.