I keep getting a weird number (chem 111)

Question

a gas occupies 56.44L at 2.00 atm and 310 K. if the gas is compressed to 23.52L and the temperature is lowered to 281 K, what is the new pressure?

When i work this problem out, I keep getting 418068.7415 which I just know doesn’t look right.

Thanks in advance!

Answer 1

PV = nRT so n = (PV)/(RT)

In an enclosed system the number of moles stays the same so we can say (P₁V₁)/(RT₁) = (P₂V₂)/(RT₂) but since R stays the same for both times 1 and times 2 we can say (P₁V₁)/(T₁) = (P₂V₂)/(T₂)

Solving for P₂ we get: P₂ = (P₁V₁T₂)/(V₂T₁)

Plug in the numbers making sure the corresponding units are the same and temp is in Kelvin:

P₂ = (2)(56.44)(281)/[(23.52)(310) = 31719.28/7291.2 = 4.35 atm

I see your mistake. This is common on the TI-84 calculator. You typed in 2*56.44*281/23.52*310 but the calculator is thinking the last "*310" is multiplying your results by 310 when you had intended to divide your results by 310. To make sure you don't fall into this trap again, you either MUST use parentheses in the denominator or just use multiple division signs (so like 2*56.44*281/23.52/310 - see the / prior to the 310?)