PROBLEM 58P
Use the combined gas law to complete the table (assume the number of moles of gas to be constant).
P1 
V1 
T1 
P2 
V2 
T2 
1.01 atm 
2.7 °C 
0.54 atm 
0.58 L 
42.3 °C 

123 torr 
41.5 mL 
626 torr 
36.5 mL 
205 K 

1.879 L 
20.8 °C 
0.412 atm 
2.05 L 
48.1 °C 
Solution 58P
Step 1:
Here we have to Use the combined gas law to complete the table (assume the number of moles of gas to be constant). First let’s see what is combined gas law :
When we put Boyle's law, Charles' law, and GayLussac's law together, we come up with the combined gas law. It shows that :
‘The ratio between the pressurevolume product and the temperature of a system remains constant’. 
This can be stated mathematically as:
= k
Where,
P = pressure,
V = volume,
T = temperature measured in kelvins,
k = constant (with units of energy divided by temperature).
For comparing the same substance under two different sets of conditions, the law can be written as:
=
Step 2:
First, let’s consider the 1st row :
We have to find V1 :
Temperature here is given in o C, let’s convert to K :
T1 = 2.7 o C + 273 = 275.7 K
T2 = 42.3 o C + 273 = 315.3 K
Using combined gas law, let’s find V1 :
V1 =
V1 = 0.27 L.
Step 3:
Now, let’s consider the 2nd row :
We have to find T1 :
Here, Pressure is given in torr , let’s convert to atm :
1 atm = 760 torr
P1 = 123 torr.
Therefore, 123 torr in atm is :
= 123 torr
P1= 0.161 atm.
P2 = 626 torr.
Therefore, 626 torr in atm is :
= 626 torr
P2= 0.823 atm.
V1 and V2 are given in mL, let’s convert to L :
V1 = 41.5 mL
We know, 1 L = 1000 mL
Therefore, 41.5 mL in L is :
= 41.5 mL
V1 = 0.0415 L
V2 = 36.5 mL
36.5 mL in L is :
= 36.5 mL
V2 = 0.0365 L
Using combined gas law, let’s find T1 :
T1 =
T1 = 45.59 K.