How to solve a combined gas law problem? (Not asking for answers to homework)?

I missed a few days and so now I'm trying to catch up. Am I doing this right?

"If I have 21 liters of gas held at a pressure of 78atm and a temp. Of 900K, what will be the volume of the gas if I decrease the pressure to 45 ATM and decrease the temp. To 750k?

(78atm)(21L)/900k = (45atm)(V2)/750
(21L)(750)(78)➗(900K)➗(45atm)=V2
30.3L=V2

I feel like I'm doing it right but when I get to the next problem my answer isn't logical....

"If I have 2.9L of gas at a pressure of 5atm and a temp. Of 50 degrees Celsius; what will the temp. Of the gas be if I decease the volume of the gas to 2.4L and decrease the pressure to 3atm? "

(5atm)(2.9L)/323=(3atm)(2.4L)/T2
(325K)(5atm(2.9L)➗(2.4aK)➗(3atm)= T2
654.5K=T2

I think my math is right but assuming this is an ideal gas shouldn't T2 be smaller than T1? We have decreased both volume and pressure; both of which are directly proportional to temperature in an ideal gas. Right!? Or am I lost entirely?

First is fine.

In the second, you're not moving things around properly. On the left the "5atm * 2.9L" is in the numerator and "323K" is in the denominator. Then in the next line, they're on the same side.


5atm * 2.9L / 323K = 3atm * 2.4L / T2
T2 = 3atm 2.4L 323K / (5atm 2.9L)
T2 = 160K

323K*.

Hello Olivia : The equation shown below works great for such a problem :
---------------------------------------...

( P2 ) ( V2 ) / ( T2 ) = ( P1 ) ( V1 ) / ( T1 ) = nR

V2 = ( V1 ) ( P1 / P2 ) ( T2 / T1 )

V2 = ( 21 L ) ( 78 atm / 48 atm ) ( 750 K / 900 K )

V2 = 28.4 L <-----

T2 = ( T1 ) ( P2 / P1 ) ( V2 / V1 )

T2 = ( 323.2 ) ( 3 atm / 5 atm ) ( 2.4 L / 2.9 L )

T2 = 160.5 K <--------------------------

The equation used requires :

( 1 ) Ideal gas
( 2 ) fixed mass or moles of the gas
( 3 ) the use of absolute temperatures
( 4 ) the use of absolute pressures