Step-by-step explanation:
To calculate the pressure inside the container, we can use the ideal gas law, which relates the pressure (P), volume (V), temperature (T), and number of moles (n) of a gas:
PV = nRT
where R is the gas constant. Assuming the container is a sealed system with a fixed amount of gas, the number of moles and volume will remain constant, so we can rearrange the equation to solve for the final pressure (P2):
P2 = (nRT2) / V
where T2 is the final temperature in Kelvin. To convert Celsius to Kelvin, we simply add 273.15.
First, let's convert the initial temperature and pressure to SI units (Kelvin and Pascals):
T1 = 1.0C + 273.15 = 274.15 K
P1 = 750 mmHg * 133.322 Pa/mmHg = 99991.5 Pa
Next, we'll convert the final temperature to Kelvin:
T2 = 80C + 273.15 = 353.15 K
We also need to know the volume of the container. If we assume it is a rigid container (i.e. the volume does not change), then we can cancel it out in the equation. Otherwise, we would need to know how the volume changes with temperature and pressure.
Assuming the volume is constant, we can plug in the values and solve for P2:
P2 = (nRT2) / V
= (nR(T1 + T2)) / V (since n, R, and V are constant)
= (P1(T1 + T2)) / T1 (since PV = nRT)
Plugging in the values:
P2 = (99991.5 Pa * (274.15 K + 353.15 K)) / 274.15 K
= 1.234 x 10^5 Pa
Therefore, the pressure inside the container at 80C is approximately 123.4 kPa.