The gaseous state

Describe the arrangement and movement of particles in a gas and explain why gases exert a pressure

The arrangement and movement of particles in a gas will be particles that are far apart and can move freely in all directions with a random arrangement.

The collisions between gas particles and the walls of the container causing gases to exert a pressure.

Two assumptions made about ideal gas behaviour are that ideal gases have zero particle volume and no intermolecular forces of attraction 

Explain why helium comes very close to ideal gas behaviour.

It does not create bonds with other atoms since its outer shell is complete. Simultaneously, it has Van der Waals’ forces due to having only two electrons.

The ideal gas equation is pV = nRT where R is the molar gas constant with a value of 8.31 J K^-1 mol^-1.

Explain as fully as you can the meaning of the following terms, and give the units for each to correspond with the value of R.

p is the pressure of the gas (Pa or N m^-2)

V is the volume occupied by gas (m³)

T is the absolute temperature of gas (K)

Calculate the volume, in dm³ , of one mole of helium gas at 10 °C and 92.0 kPa. Give your answer to 3 significant figures. Show your working.

p = `92 xx 10^3` Pa and T = `273 + 10 = 283` K

`pV = nRT -> V = (nRT)/p = (1xx8.31xx283)/(92xx10^3) = 0.02556 m^3 = 25.6 dm^3`

1.85 g of white phosphorus was reacted with 75.00 cm³ of 1.25 mol dm^-3 sodium hydroxide solution to make phosphine.

`P_4(s) + 3OH^(-) (aq) + 3H_2O(l) -> PH_3(g) + 3H_2PO""_2^(-) (aq)`

Deduce which chemical is the limiting reagent.

Moles of `P_4 = (mass)/(M_r) = 1.85 / (4xx31.0) = 0.0149` mol

Moles of `OH^- = 0.07500 xx 1.25 = 0.09375` mol 

0.0149 mols of P₄ react with 0.0447 moles of OH^-

Thus, P4 is the limiting reagent.

The `M_r` value of a gas can be calculated from the general gas equation. Which expression will give the value of `M_r` for a sample of a gas of mass m grams?

A. `M_r = (mRT)/(pV)`

B. `M_r = (pVRT)/m`

C. `M_r = (mpV)/(RT)`

D. `M_r = (pV)/(mRT)`

The answer is A.

We have:

`pV = nRT = (mRT)/(M_r) => M_r = (mRT)/(pV)`

0.96 g of hydrogen gas is contained in a sealed vessel of volume of 7.0 × 10^-3 m³ at a temperature of 303 K. Assume the gas behaves as an ideal gas. What is the pressure of the vessel?

A. 172.7 Pa

B. 172.7 kPa

C. 345.5 Pa

D. 691.1 kPa

The answer is B.

We have:

`pV = nRT => p = (nRT)/V = (mRT)/(M_rV) = (0.96xx8.314xx303)/(2xx1.0xx7.0 × 10^-3) = 172741 Pa = 172.7 kPa`

A 5370 cm³ sample of oxygen is measured at a temperature of 60 °C. The pressure measured was 103000 Pa. 

Assume the gas behaves as an ideal gas. 

What is the mass of the sample of oxygen?

A. 3.2 g

B. 6.4 g

C. 1.8 g

D. 3.6 g

The answer is B.

We have

V = 5370 cm³ = `5370 xx 10^-6` m³

T = `60 + 273 = 333` K

`pV = nRT = (mRT)/(M_r) => m = (pVM_r)/(RT) = (103000xx5370xx10^-6xx16.0xx2)/(8.314xx333) = 6.4 g`

A sample of chlorine gas with a of mass 5.35 g has a volume of 1.247 × 10^-3 m³ at a pressure of 1.00 × 10⁵ Pa.

Assuming the gas acts as an ideal gas, what is the temperature of the gas?

A. 300 K

B. 250 K

C. 100 K

D. 200 K

The answer is D.

We have

`pV = nRT => T = (pV)/(nRT) = (M_rpV)/(mRT) = (2xx35.5xx1.00xx10^5xx1.247xx10^-3)/(5.35xx8.314) = 200 K`

A bubble travelled up from the sea bed to the surface. Just below the surface of the sea the bubble had a volume of 200 cm³ at a pressure of 101 kPa, the temperature at the surface is the same as the sea bed.

The pressure at the sea bed is 2020 kPa.

What is the volume of the bubble at the sea bed?

A. 10 cm³

B. 200 cm³

C. 100 cm³

D. 1000 cm³

The answer is A.

The temperature and moles remain constant.

With the surface, p₁V₁ = nRT

With the sea bed, p₂V₂ = nRT

Thus, `p_1V_1 = p_2V_2 => V_2 = (p_1V_1)/(p_2) = (101xx200xx10^-6)/2020 = 1xx10^-5 m^3 = 10 cm^3`