Ideal gas calculations

Remember that the volume in the ideal gas law equation has to be quoted in m³.

There are 1000000 cm³ in 1 m³. This means that the 30 cm³ must be entered as 30 / 1000000 or 0.00003 or 3 x 10 ^-5  m³

If  temperature of a container is 48 ^oC.this must be entered into the ideal gas equation as the absolute temperature so that means in Kelvin. The temperature in Kelvin is found by adding 273 to the temperature in ^oC.

So, 48 ^oC becomes 48 + 273 = 321 K 

Remember: R = 8.31 JK^-1mol^-1, 0 K = -273 ^oC

1.Calculate the volume occupied by one mole of a gas at 25 ^oC and 100 kPa.

2.Calculate the pressure of a gas given that 0.2 moles of the gas occupy 10 dm³ at 20 ^oC.

3.Calculate the temperature of a gas if 0.5 moles occupy 1.2 dm³ at a pressure of 200 kPa.

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

5.Calculate the relative molecular mass of a gas if a 500 cm³ sample at 20 ^oC and 1 atm has a mass of 0.66 g.

6.At 25 ^oC and 100 kPa a gas occupies a volume of 20 dm³. Calculate the new temperature of the gas if

a)the volume is decreased to 10 dm³ at constant pressure.

b)the pressure is decreased to 50 kPa at constant volume.

7. 10.0 g of calcium nitrate is heated at 100 kPa and a temperature of 300 ^oC, at which temperature it fully decomposes. Calculate

a) the volume of nitrogen dioxide evolved

b) the volume of oxygen evolved

c) the total volume of gas evolved

Equation: 2Ca(NO₃)₂(s) à 2CaO(s) + 4NO₂(g) + O₂(g)

8. Calculate the volume of oxygen produced at 298 K and 100 kPa by the decomposition of 30 cm³ of 0.1 moldm^-3 hydrogen peroxide.

Equation: 2H₂O₂(aq) à 2H₂O(l) + O₂(g)

9. Lead (IV) oxide dissolves in concentrated hydrochloric acid according to the following equation: PbO₂(s) + 4HCl(aq) à PbCl₂(s) + Cl₂(g) + 2H₂O(l)

Starting with 37.2 g of lead (IV) oxide, calculate:

a) the volume of 12 moldm^-3 HCl needed to completely dissolve it

b) the mass of PbCl₂ produced

c) the volume of chlorine produced at 298 K and 100 kPa.

10.What mass of magnesium, and what volume of 2.0 moldm^-3 hydrochloric acid, will be required to produce 100 cm³ of hydrogen gas at 298 K and 100 kPa?

Equation: Mg(s) + 2HCl(aq) à MgCl₂(aq) + H₂(g)

11.0.52 g of sodium was added to 100 cm³ of water. Calculate:

a)The volume of hydrogen evolved at 298 K and 100 kPa

b)The concentration of the sodium hydroxide solution produced, assuming the volume of water does not change.

Equation: 2Na(s) + 2H₂O(l) à 2NaOH(aq) + H₂(g)