Measuring a Gas Law

A gas has no shape, no fixed volume, and almost no mass you can feel. It is the least substantial thing in the room and it obeys the tidiest arithmetic in the course. Today you find that arithmetic yourself, from readings you take, and then you use it to weigh something you cannot see.

Two parts. In the first you squeeze or heat a fixed amount of gas and look for the relationship. In the second you make a gas from a weighed piece of metal, measure its volume, and work out how much room one mole of it takes up.

What you are trying to find out

Part A. A sample of gas has a pressure, a volume, and a temperature. Change one, hold one fixed, and watch the third. Is the relationship a straight line? Through the origin? What has to be true of your temperature scale for the question “through the origin” to even make sense?¹

Part B. Magnesium and dilute hydrochloric acid give hydrogen:

$\mathrm{Mg}(\mathrm{s})+2\mathrm{HCl}(\mathrm{aq})\to \mathrm{MgCl}{}_2(\mathrm{aq})+\mathrm{H}{}_2(\mathrm{g})$

Weigh the magnesium and the equation tells you how many moles of hydrogen you made. Measure the volume that hydrogen occupies and you have the molar volume of a gas — the room one mole takes up — under the conditions in your room, on the day you measured it.

That last clause is not padding. A molar volume without its conditions attached is a meaningless number, and half the marks on this page live in remembering to attach them.

What you have to work with

Part A — choose one and design it

• Pressure and volume. A gas syringe or a large plastic syringe with a sealed tip, mounted, with slotted masses that can be added to the plunger up to the limit stated on your station card. Read the volume as the load changes.
• Volume and temperature. A narrow tube containing a short column of gas trapped by a liquid index, open at the top, in a water bath. Measure the length of the gas column at several bath temperatures.

Part B — the molar volume of hydrogen

• Magnesium ribbon, cleaned, and a balance reading to 0.001 g if the room has one
• Dilute hydrochloric acid, 1.0 mol/L
• A gas collection setup — a eudiometer over water, or a gas syringe connected to a small flask
• Thermometer, and the room’s barometer or the current local pressure
• A table of the vapour pressure of water at various temperatures, supplied at the station

Your design decisions, written down and checked before you run anything:

• Which variable you hold constant in Part A, and how you actually hold it. The syringe warms in your hand; a water bath takes minutes to reach equilibrium. Say what you will do about each.
• How many points you will take, and over what range. Two points make a line whether or not the relationship is linear. Five make a claim.
• The mass of magnesium, chosen so the hydrogen volume fits your apparatus with room to spare. Show the calculation. A gas syringe that runs out of travel mid-reaction gives you nothing, and a piece too small puts your mass inside the balance’s resolution.
• How you will get the gas pressure right. Gas collected over water is not dry, and gas in a tube standing above the trough is not at atmospheric pressure. Both have fixes and you should know them before you need them.

Hydrogen burns, and nothing here is ever sealed and heated

• Part B produces hydrogen gas, which is flammable across a wide range of mixtures with air. There are no flames, no burners, no hot plates, and no sparks anywhere in the room while any group is collecting gas. Vent the collected gas into the fume hood or out an open window at the end, away from everyone.
• Nothing that makes gas is sealed in a rigid container, ever. The collection apparatus is open to the atmosphere by design — through the water in the trough, or through the syringe’s travel. Do not clamp, cap, or block it.
• Never heat a sealed system. The Part A syringe has a sealed tip and a movable piston, which is a designed pressure vessel with a stated load limit. Do not exceed the masses listed on your station card, do not hold the plunger down, and do not bring it anywhere near a heat source.
• Water baths stay below 60 °C. Hot water scalds, glass that goes from a hot bath to a cold bench can crack, and hot glassware looks exactly like cold glassware. Tongs.
• The acid is 1.0 mol/L hydrochloric acid, the school dilution. Eye protection throughout, including cleanup. If you need to dilute anything, add acid to water, never water to acid — the heat has somewhere to go when the water is already there.
• Never pipette by mouth. Bulb or pump.
• The magnesium reaction warms the flask, and a warmed gas reads a larger volume. Wait for it to return to room temperature before your final reading. This is a safety point and a measurement point at once.
• Waft, do not sniff. Nothing is tasted. Waste to the labelled containers, and nothing back into a stock bottle.
• Report every spill, splash, and surprise immediately.

The prediction you write first

Before any reading is taken:

1. Part A: sketch the graph you expect, axes labelled with units, and say whether it passes through the origin. Then say what a straight line through the origin would mean physically.
2. The relationship you expect between your two variables, written as a proportionality with a stated constant.
3. Part B: the volume of hydrogen you expect from the mass of magnesium you chose, in millilitres, with the working shown. State the temperature and pressure your prediction assumes.
4. The molar volume you expect to measure, in L/mol, and the conditions you are quoting it at. Commit to a number.
5. Which direction you expect to be wrong in, and why.

What to collect

Part A

Trial	Controlled variable and its value	Independent variable, with units	Dependent variable, with units	Temperature (K)
1
2
3
4
5

Every temperature in kelvins, converted at the moment you record it, with the Celsius reading kept alongside so the conversion can be checked. Every column headed with a unit. Graph it, and graph the version you think should be linear — if you suspect an inverse relationship, plot against the reciprocal and see whether the line straightens.

Part B

Measurement	Value	Unit	Resolution
Mass of magnesium		g
Room temperature at the final reading		°C
Room temperature		K	—
Atmospheric pressure		kPa
Vapour pressure of water at that temperature		kPa	—
Pressure of the dry hydrogen		kPa	—
Volume of gas collected		mL

Two corrections turn a raw reading into a measurement, and both are worth understanding rather than applying.

Levelling. If you collected over water, raise or lower the tube until the water inside is at the same height as the water in the trough before you read the volume. Only then is the gas inside at atmospheric pressure, which is the pressure you are about to write down.

Water vapour. Gas collected over water carries water vapour with it. The total pressure is atmospheric, but part of that belongs to the vapour, so the hydrogen’s own pressure is atmospheric pressure minus the vapour pressure of water at your temperature. Look it up on the table at your station and subtract it.

Then:

$n=\frac{m}{M}{V}_{\text{molar}}=\frac{V}{n}\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

Use the first to get moles of hydrogen from the mass of magnesium, the second to get the molar volume at your room’s conditions, and the third to convert that to a stated set of standard conditions so it can be compared with anyone else’s.

State your conditions every time you quote a molar volume. Written without them, the number is not wrong — it is not a number.

What to bring to the consolidation discussion

• Part A: your table, your graph, and the relationship you are claiming, written as an equation with a constant that has units.
• The value of that constant, and one sentence on what it depends on.
• Part B: your molar volume at your measured conditions, and converted to standard conditions, with both sets of conditions stated.
• The percentage difference between your value and the accepted molar volume at those same conditions.
• Which corrections you applied and how much each one changed the answer, in millilitres or kilopascals. A correction you applied without knowing its size is a ritual.

What you should not claim

• Five points and a ruler do not establish a law. They establish that your data are consistent with a straight line over the range you covered, at one temperature, with one gas, in one afternoon. Say that.
• A gas law is a model, and models have edges. Nothing you measured today probes what happens at high pressure or near the temperature where your gas would liquefy, which is exactly where the tidy arithmetic stops working.
• Uncorrected water vapour pushes the molar volume up. If you forgot to subtract the vapour pressure, you used too large a pressure for the hydrogen and your converted volume comes out too large. It is usually a small correction and it is a real one, and being able to say which way it goes is worth more than applying it silently.
• A gas read while the flask was still warm reads too large, so the molar volume comes out high again. Between this and the vapour pressure, the common errors in Part B share a direction, which is worth saying out loud in your conclusion.
• Magnesium ribbon carries an oxide coating, and that pushes the other way. Some of the mass you weighed was not magnesium, so you thought you had more moles of hydrogen than you did, and the molar volume comes out low. Whether your result lands high or low depends on which of these dominates, and you can estimate that.
• Do not report more figures than your weakest instrument supports. A volume read from a eudiometer to the nearest 0.2 mL and a mass to the nearest 0.001 g do not combine into a molar volume good to five digits. Round at the end, once.

Curriculum connection

F2.2

determine, through inquiry, the quantitative and graphical relationships between the pressure, volume, and temperature of a gas [PR, AI]

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F2.5

determine, through inquiry, the molar volume or molar mass of a gas produced by a chemical reaction (e.g., the molar volume of hydrogen gas from the reaction of magnesium with hydrochloric acid) [PR, AI]

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A1.12

use appropriate numeric, symbolic, and graphic modes of representation, and appropriate units of measurement (e.g., SI and imperial units)

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Footnotes

1. You will be told to convert to kelvins and it will feel like bookkeeping. It is not. A proportionality — “double this and that doubles” — only means anything on a scale whose zero corresponds to none of the quantity. The Celsius zero is the freezing point of water, picked because it is convenient in a kitchen, and it has nothing to do with a gas having no thermal energy. Doubling a temperature from 20 °C to 40 °C doubles nothing physical, which is exactly why a graph of volume against Celsius temperature is a straight line that misses the origin, and a graph against kelvins is a straight line through it. Where that line crosses zero volume is worth extrapolating to and thinking about. ↩