Ideal gas equation and moles questions

1)    If I have 40 moles of a gas at a pressure of 56000 Pa and a volume of 2 m3, what is the temperature?

P V = n R T                                             Rearrange to get T on its own, divide both sides by n R

T  =  P V

n R

T  =  56000  x  2

40  x  8.31

T  =   337 K

2)    If I have an unknown quantity of gas at a pressure of 120000 Pa, a volume of 31 dm3, and a temperature of 360 k, how many moles of gas do I have?

Convert units to SI units first:                       V  =  31 x 10-3 m3

P V = n R T                                             Rearrange to get n on its own, divide both sides by RT

n  =  P V

R T

n  =  120000  x  31 x 10-3

8.31  x  360

n  =   1.24 moles

3)    If I contain 3 moles of gas in a container with a volume of 60 dm3 and at a temperature of 400 K, what is the pressure inside the container?

Convert units to SI units first:                       V  =  60 x 10-3 m3

P V = n R T                                             Rearrange to get P on its own, divide both sides by V

P  =  n R T

V

P  =  3  x  8.31  x  400

60 x 10-3

P  =  166200 Pa

4)    If I have 7.7 moles of gas at a pressure of 9 kPa and at a temperature of 56 0C, what is the volume of the container that the gas is in?

Convert units to SI units first:                       P  =  9 x 103 Pa        T  =  56 + 273 = 329 K

P V = n R T                                             Rearrange to get V on its own, divide both sides by P

V  =  n R T

P

V  =  7.7  x  8.31  x  329

9 x 103

V  =  2.34 m3

5)    An unknown gas weighs 34g and occupies 6.7 dm3 at 200 kPa and 245K. What is its relative molecular mass?

To calculate Mr from mass, you need moles from the ideal gas equation first:

Convert units to SI units first:                       V  =  6.7 x 10-3 m3   P  =  200 x 103

P V = n R T                                             Rearrange to get n on its own, divide both sides by RT

n  =  P V

R T

n  =  200 x 103  x  6.7 x 10-3

8.31  x  245

n  =   0.658 moles

now use these moles in the mass / moles formula:

Mr  =  mass

n

Mr  =  34

0.658

Mr  =  51.7g mol-1

6)    What is the volume of 23g of argon gas at 1 oC and a pressure of 200 kPa?

You cannot calculate volume directly from a mass so mass must be converted to moles to use in the gas equation first

n  =  mass

Ar

n  =  23

39.9

n  =  0.576

now use these moles in the ideal gas equation:

Convert units to SI units first:                       P  =  200 x 103 Pa   T  =  1 + 273 = 274 K

P V = n R T                                             Rearrange to get V on its own, divide both sides by P

V  =  n R T

P

V  =  0.576  x  8.31  x  274

200 x 103

V  =  6.56 x 10-3 m3

7)    Calculate the mass of a sample of carbon dioxide which occupies 20 dm3 at 27 oC and 100 kPa.

To calculate mass you’ll need moles, n from the ideal gas equation first:

Convert units to SI units first:                       V  =  20 x 10-3 m3    P  =  100 x 103         T  =  27 + 273 = 300

P V = n R T                                             Rearrange to get n on its own, divide both sides by RT

n  =  P V

R T

n  =  100 x 103  x  20 x 10-3

8.31  x  300

n  =   0.802 moles

now use these moles in the mass / moles formula to calculate mass:

mass  =  n  x  Mr

mass  =  0.802  x  44

mass  =  35.3 g

8)    Calculate the relative molecular mass of a gas if a 500 cm3 sample at 20 oC and 100 kPa has a mass of 0.66 g.

To calculate Mr from mass, you need moles from the ideal gas equation first:

Convert units to SI units first:                       V  =  500 x 10-6 m3  P  =  100 x 103         T  =  20 + 273 = 293

P V = n R T                                             Rearrange to get n on its own, divide both sides by RT

n  =  P V

R T

n  =  100 x 103  x  500 x 10-6

8.31  x  293

n  =   0.0205 moles

now use these moles in the mass / moles formula:

Mr  =  mass

n

Mr  =  0.66

0.0205

Mr  =  32.1 g mol-1