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1.2.2 Relative molecular mass and rate of diffusion

Relative molecular mass

Definition

Relative molecular mass

The sum of the relative atomic masses of all the atoms shown in the formula of a molecule, given the symbol MrM_rMr​.

  1. The particles of different gases have different masses, and the relative molecular mass, MrM_rMr​, is used to compare them.
  2. To find MrM_rMr​, add together the relative atomic masses, ArA_rAr​, of every atom shown in the formula of the molecule.
  3. The ArA_rAr​ values are read from the Periodic Table, for example H=1\text{H}=1H=1, C=12\text{C}=12C=12, N=14\text{N}=14N=14, O=16\text{O}=16O=16 and Cl=35.5\text{Cl}=35.5Cl=35.5.
  4. MrM_rMr​ has no units, because it compares masses rather than measuring them.
  5. A gas with a larger MrM_rMr​ is made of heavier particles than a gas with a smaller MrM_rMr​.
Example

Calculating relative molecular masses

  • Ammonia, NH3\text{NH}_3NH3​, contains one nitrogen atom and three hydrogen atoms.
Mr(NH3)=14+(3×1)=17 M_r(\text{NH}_3)=14+(3\times1)=17 Mr​(NH3​)=14+(3×1)=17
  • Hydrogen chloride, HCl\text{HCl}HCl, contains one hydrogen atom and one chlorine atom.
Mr(HCl)=1+35.5=36.5 M_r(\text{HCl})=1+35.5=36.5 Mr​(HCl)=1+35.5=36.5
  • Carbon dioxide, CO2\text{CO}_2CO2​, contains one carbon atom and two oxygen atoms.
Mr(CO2)=12+(2×16)=44 M_r(\text{CO}_2)=12+(2\times16)=44 Mr​(CO2​)=12+(2×16)=44

Molecular mass and rate of diffusion

Definition

Rate of diffusion

How quickly a substance spreads out by diffusion, measured as the distance its particles travel in a given time.

  1. At the same temperature, the particles of every gas have the same average kinetic energy.
  2. The kinetic energy of a moving particle depends on both its mass and its speed.
  3. For a heavy particle and a light particle to have the same kinetic energy, the heavy particle must move more slowly and the light particle must move faster.
  4. Particles that move faster spread out among the air particles more quickly, so their gas diffuses faster.
  5. Therefore, at the same temperature, a gas with a lower MrM_rMr​ has a higher rate of diffusion than a gas with a higher MrM_rMr​.
  6. The rate of diffusion decreases as the relative molecular mass of a gas increases.
  7. Hydrogen, with Mr=2M_r=2Mr​=2, is the lightest gas, so it diffuses faster than any other gas at the same temperature.
  8. The comparison is only fair when the gases are at the same temperature, because raising the temperature makes every gas diffuse faster.
Common Mistake

Do not say that a heavier gas diffuses more slowly because gravity pulls it down, because the difference comes from the lower speed of its particles at the same temperature.

Example

Ranking gases by rate of diffusion

  • Hydrogen, methane, oxygen and chlorine are compared at room temperature by first working out the MrM_rMr​ of each gas.
Mr(H2)=2×1=2 M_r(\text{H}_2)=2\times1=2 Mr​(H2​)=2×1=2 Mr(CH4)=12+(4×1)=16 M_r(\text{CH}_4)=12+(4\times1)=16 Mr​(CH4​)=12+(4×1)=16 Mr(O2)=2×16=32 M_r(\text{O}_2)=2\times16=32 Mr​(O2​)=2×16=32 Mr(Cl2)=2×35.5=71 M_r(\text{Cl}_2)=2\times35.5=71 Mr​(Cl2​)=2×35.5=71
  • The lower the MrM_rMr​, the faster the gas diffuses, so the order from fastest to slowest is hydrogen, methane, oxygen and then chlorine.

Ammonia and hydrogen chloride

  1. Ammonia and hydrogen chloride are both colourless gases that react as soon as they meet to form a white solid called ammonium chloride.
  2. The equation for the reaction is NH3(g)+HCl(g)→NH4Cl(s)\text{NH}_3(\text{g})+\text{HCl}(\text{g})\rightarrow\text{NH}_4\text{Cl}(\text{s})NH3​(g)+HCl(g)→NH4​Cl(s).
  3. When the two gases are released at opposite ends of a long glass tube, each one diffuses along the tube towards the other.
  4. A white ring of ammonium chloride forms at the point inside the tube where the two gases meet.
  5. The ring forms closer to the hydrogen chloride end, because ammonia, with Mr=17M_r=17Mr​=17, diffuses faster than hydrogen chloride, with Mr=36.5M_r=36.5Mr​=36.5, and so travels further in the same time.
  6. The ring takes several minutes to appear, even though the gas particles move at hundreds of metres per second, because each particle collides with air particles an enormous number of times and keeps changing direction.
Practical

Comparing the rates of diffusion of two gases

  • Aim: to show that a gas with a lower MrM_rMr​ diffuses faster, by comparing the distances travelled by ammonia and hydrogen chloride along a tube.
  • Apparatus: a clean, dry glass tube about 1 m1\ \text{m}1 m long, two rubber bungs that fit the ends of the tube, two clamp stands, cotton wool, two pairs of forceps, concentrated aqueous ammonia, concentrated hydrochloric acid, a metre rule, a stopwatch, a fume cupboard, eye protection and gloves.
  • Method:
    • Clamp the tube horizontally inside a fume cupboard, so that it is level and will not be moved during the experiment.
    • Using forceps, soak one small piece of cotton wool in concentrated aqueous ammonia and another in concentrated hydrochloric acid.
    • Working with a partner, push the ammonia cotton wool into one end of the tube and the hydrochloric acid cotton wool into the other end at the same moment.
    • Close both ends of the tube with the rubber bungs straight away, and start the stopwatch.
    • Watch the tube without disturbing it until a white ring appears, then record the time.
    • Measure the distance from each piece of cotton wool to the white ring with the metre rule.
  • Results: a white ring of ammonium chloride forms after a few minutes, roughly 60 cm60\ \text{cm}60 cm from the ammonia end and 40 cm40\ \text{cm}40 cm from the hydrochloric acid end of a 1 m1\ \text{m}1 m tube.
  • Conclusion: ammonia travels further than hydrogen chloride in the same time, so ammonia diffuses faster, which matches its lower MrM_rMr​.
  • Sources of error: inserting the two pieces of cotton wool at different times gives one gas a head start, a damp tube absorbs some of each gas because both are very soluble in water, and any draught or movement of the tube disturbs the gases.
  • Safety: both concentrated solutions give off choking, corrosive fumes, so work in a fume cupboard, wear eye protection and gloves, and handle the cotton wool only with forceps.
Exam technique

Explaining differences in rate of diffusion

  • Work out or quote the MrM_rMr​ of both gases before you compare them, so that your comparison is backed by numbers.
  • State which gas has the lower MrM_rMr​, and say that its particles are lighter and therefore move faster at the same temperature.
  • Link the faster-moving particles to a faster rate of diffusion, or to a greater distance travelled in the same time.
  • In the tube experiment, state that the ring forms nearer the end where the gas with the higher MrM_rMr​ was released, because that gas travels the shorter distance.
Self review
  • Calculate the MrM_rMr​ of ammonia, NH3\text{NH}_3NH3​.
  • State how the rate of diffusion of a gas changes as its relative molecular mass increases.
  • Explain why lighter gas particles move faster than heavier gas particles at the same temperature.
  • Name the white solid that forms when ammonia meets hydrogen chloride.
  • Explain why the white ring in the diffusion tube forms closer to the hydrochloric acid end.
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1.2.2 Relative molecular mass and rate of diffusion Revision Guide

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Revision notes for CIE IGCSE Chemistry 1.2.2 Relative molecular mass and rate of diffusion: explanations and worked examples.

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