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# Use the combined gas law to complete the table (assume the ISBN: 9780321910295 34

## Solution for problem 58P Chapter 11

Introductory Chemistry | 5th Edition

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Problem 58P

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
Step-by-Step Solution:

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 Gay-Lussac's law together, we come up with the combined gas law. It shows that :

 ‘The ratio between the pressure-volume 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.

Step 4 of 5

Step 5 of 5

##### ISBN: 9780321910295

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