How do you calculate the final pressure, and how do you convert a negative mmHg?

Question

Answer 1

Use PV=nRT, the ideal gas law. P1 and T1 can be initial pressure and temperature, and P2 and T2 the final pressure and temperature. We are given P1, T1, and T2. We do not know the volume, but since it is constant, we can just us V, without indicating V1 or V2. We can use the ideal gas law to solve for the one variable which is not a constant (like R) or given (P1 and T1). If we rearrange the equation to solve for V, we get V=nRT1/P1, and also V=nRT2/P2. We set these equal to one another since V is constant: nRT1/P1 = nRT2/P2. Since n and R are present on both sides, we can divide both sides by nR, to simplify the equation to T1/P1=T2/P2. This implies that (-70 C)/780 mmHg = (30 C)/P2. However, T needs to be in Kelvin, not Celcius, so we will convert by adding 273.15 to the value in celcius. This gives us the absolute temperature, and by plugging those values in for T1 and T2, we find that P2=((30 + 273.15) K)(780 mmHg)/(-70 + 273.15 K). The units of Kelvin cancel and we get an answer for P2 in mmHg, which serves as a nice confirmation that at least our units worked out right. Solve that for the answer.