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Química Geral · Reactions in water and gases

Leis dos gases e estequiometria de gases

Uma lição resolvida gratuita e 40 problemas de prática em que você mesmo desenha cada seta curva.

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O que você vai aprender

  • Convert between pressure units and read pressures from barometers, open-end and closed-end manometers and gauges.
  • Apply Boyle's, Charles's, Gay-Lussac's and Avogadro's laws and the combined gas law, always with absolute temperature.
  • Use the ideal gas law PV = nRT and the molar volume at STP (0 °C and 1 atm, 22.41 L/mol) to relate pressure, volume, temperature and amount.
  • Calculate gas densities and find molar masses and molecular formulas from density or vapour data.
  • Combine balanced equations with gas volumes to solve stoichiometry and limiting-reactant problems.

Lição gratuita

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Pressure and how it is measured

Pressure is force per unit area. The SI unit is the pascal (1 Pa = 1 N/m²); chemists also use 1 atm = 101.325 kPa = 760 torr = 760 mmHg, and 1 bar = 100 kPa exactly. A mercury barometer is a sealed tube inverted in a dish of mercury: the column falls until its weight per unit area balances the atmosphere, about 760 mm at sea level. The height depends only on the pressure and the density of the liquid, not on the width of the tube, so a column of a liquid with density ρ is taller than the mercury column by the factor 13.6/ρ (mercury 13.6 g/cm³): water would stand about 10.3 m high. A manometer compares a gas with a reference. In an open-end manometer the other arm is open to the air: if the mercury on the gas side stands h mm lower, the gas pushes harder and P(gas) = P(atm) + h; if it stands higher, P(gas) = P(atm) − h. In a closed-end manometer the other arm is evacuated, so P(gas) = h directly. A column of another liquid is converted to mmHg by multiplying its height by ρ(liquid)/ρ(Hg). A tyre gauge reads gauge pressure, the excess above atmospheric pressure; the gas laws always need absolute pressure = gauge + atmospheric.

The simple gas laws and the combined gas law

For a fixed amount of gas: Boyle's law, P₁V₁ = P₂V₂ at constant temperature (volume is inversely proportional to pressure); Charles's law, V₁/T₁ = V₂/T₂ at constant pressure; Gay-Lussac's law, P₁/T₁ = P₂/T₂ at constant volume. Avogadro's law adds the amount: at constant T and P, V/n is constant, so equal volumes of any gases at the same T and P contain equal numbers of molecules. Temperatures must be absolute: T(K) = T(°C) + 273.15. Plots of volume against Celsius temperature are straight lines whose slopes depend on the sample, but every line extrapolates to zero volume at −273.15 °C, absolute zero; real gases condense before they get there. When several variables change at once, use the combined gas law P₁V₁/T₁ = P₂V₂/T₂. Worked example: 2.00 L of gas at 0.800 atm and 20 °C is taken to 1.60 atm and 120 °C. V₂ = 2.00 L × (0.800/1.60) × (393.15 K/293.15 K) = 2.00 × 0.500 × 1.341 = 1.34 L. Check each factor by direction: higher pressure shrinks the gas, higher temperature expands it.

The ideal gas law and molar volume

Combining the simple laws gives PV = nRT, with R = 0.08206 L·atm/(mol·K) = 8.314 J/(mol·K). Match the units to R: P in atm, V in L and T in K with 0.08206; with 8.314, P in Pa and V in m³, or equivalently P in kPa and V in L, because 1 J/L = 1 kPa. Worked example: 0.350 mol O₂ in a 5.00 L flask at 25 °C has P = nRT/V = 0.350 × 0.08206 × 298.15/5.00 = 1.71 atm. In this topic STP means 0 °C (273.15 K) and 1 atm, where one mole of any ideal gas occupies RT/P = 0.08206 × 273.15 = 22.41 L. At 25 °C and 1 atm the molar volume is 24.47 L/mol. The IUPAC convention of 0 °C and 1 bar gives 22.71 L/mol, so always check which STP a problem means. Real gases such as N₂ (drawn) follow the ideal gas law closely at ordinary temperatures and pressures; every calculation here treats the gases as ideal.

Gas density and molar mass

Substituting n = m/M into PV = nRT gives d = m/V = PM/RT. At fixed T and P a gas's density is proportional to its molar mass, so CO₂ (44.01 g/mol) is denser than air (about 29 g/mol) and He (4.00 g/mol) is far less dense. At constant pressure the density falls as the temperature rises, which is why hot air rises. O₂ (drawn) at STP has d = 32.00 g/mol ÷ 22.41 L/mol = 1.43 g/L. Rearranged, M = dRT/P identifies an unknown gas. In the Dumas method a volatile liquid is vaporised to fill a flask of known volume at a known temperature and pressure, and the mass of the condensed vapour gives M = mRT/PV. Worked example: 0.500 g of vapour fills 200.0 mL at 100.0 °C and 1.00 atm, so M = 0.500 × 0.08206 × 373.15/(1.00 × 0.2000) = 76.6 g/mol. If the empirical formula is known, divide M by the empirical-formula mass to get the molecular formula.

Stoichiometry with gases

Balanced equations relate moles, and PV = nRT turns a gas volume into moles and back. Path: mass of reactant → moles → mole ratio → moles of gas → volume at the stated T and P (or the reverse). Worked example: 1.00 g of Mg reacts with excess HCl, Mg + 2 HCl → MgCl₂ + H₂. n(H₂) = n(Mg) = 1.00/24.31 = 0.04114 mol, and at 25 °C and 1.00 atm V = nRT/P = 0.04114 × 0.08206 × 298.15/1.00 = 1.01 L. When every gas is measured at the same T and P, volumes are proportional to moles, so the coefficients give volume ratios directly (Gay-Lussac's law of combining volumes): CH₄ + 2 O₂ → CO₂ + 2 H₂O burns 1.0 L of methane (drawn with O₂) with 2.0 L of O₂. The same idea finds the limiting reactant among gases: compare the volume ratio supplied with the ratio required. Liquid or solid products have negligible volume and drop out of the gas total.

What to carry forward

Use absolute pressure and kelvin temperature every time. For one sample under changing conditions use P₁V₁/T₁ = P₂V₂/T₂; for a single state use PV = nRT with units that match R. At STP (0 °C, 1 atm) a mole of ideal gas fills 22.41 L, and at 25 °C and 1 atm 24.47 L. Density is d = PM/RT, so M = dRT/P. In reactions, convert gas volumes to moles, apply the mole ratio, and convert back; at the same T and P, volumes react in the ratio of the coefficients.

Problemas de prática (40)

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Pressure and its measurement

  • Does a wider barometer tube change the reading?Predict how the width of a barometer tube affects the height of the mercury column.

The simple and combined gas laws

  • Heating a sealed rigid flaskPredict how the pressure in a sealed rigid container changes when it is heated.

Classificar 1

  • Which gas law explains rising dough?Classify a real situation by the gas law that relates the variables that change.

Comparar 4

Ideal gas law and molar volume

  • Which sample takes up the most room?Compare gas volumes at the same temperature and pressure by converting masses to moles.

The simple and combined gas laws

  • Rank the final volumesRank the volumes of one gas sample after different simultaneous pressure and temperature changes.

Gas density and molar mass

  • Rank gases by densityRank gases by density at the same temperature and pressure using their molar masses.

Pressure and its measurement

  • Rank pressures given in different unitsRank pressures expressed in atm, kPa, torr, bar and mmHg by converting them to a common unit.

Calcular 20

The simple and combined gas laws

  • An aerosol can in a fireApply Gay-Lussac's law to find the pressure of a gas in a fixed volume after heating.
  • Compress a gas at constant temperatureApply Boyle's law to find the volume of a gas after compression at constant temperature.
  • Heat a gas at constant pressureApply Charles's law with temperatures converted to kelvin.
  • A bubble rises from the bottom of a lakeUse the combined gas law for a bubble that moves to lower pressure and higher temperature.
  • A balloon rises into cold, thin airApply the combined gas law when pressure and temperature change together.

Gas stoichiometry

  • Hydrogen from aluminium and acidCombine mass-to-mole conversion, a non-1:1 mole ratio and the ideal gas law at non-standard conditions.
  • Gas volume after a limiting-reactant reactionFind the limiting reactant from gas volumes and the total gas volume after reaction at constant temperature and pressure.
  • Oxygen from potassium chlorateUse a mole ratio and the molar volume at STP to find the volume of gas a reaction produces.
  • Oxygen needed to burn propaneApply the law of combining volumes to gases measured at the same temperature and pressure.

Gas density and molar mass

  • Density of carbon dioxide at STPCalculate the density of a gas at STP from its molar mass and the molar volume.
  • Molar mass by the Dumas methodFind the molar mass of a volatile liquid from Dumas-method vapour data with mixed units.
  • Molar mass from a gas densityCalculate the molar mass of a gas from its measured density, temperature and pressure.

Ideal gas law and molar volume

  • How empty is a high vacuum?Count the molecules in a small volume of gas at very low pressure with the ideal gas law.
  • Moles of gas in a cylinderUse PV = nRT to find the amount of gas from its pressure, volume and temperature.
  • Pressure in kilopascals with R in joulesUse R = 8.314 J/(mol·K) with consistent SI units to find a gas pressure in kilopascals.
  • Volume of nitrogen at STPConvert an amount of gas to its volume at STP with the molar volume 22.41 L/mol.
  • Find the temperature of a gasRearrange the ideal gas law to find temperature and convert it to degrees Celsius.

Pressure and its measurement

  • Convert a barometer reading to kPaConvert a pressure from torr to kilopascals through the atmosphere.
  • How tall is a water barometer?Use the density ratio of two liquids to find the column height that balances a given pressure.
  • A manometer filled with waterConvert a water-column manometer reading to torr and find the absolute gas pressure.

Encontre o erro 2

Pressure and its measurement

  • What went wrong with the tyre calculation?Diagnose the use of gauge pressure where the ideal gas law needs absolute pressure.

Ideal gas law and molar volume

  • Find the error in an ideal-gas calculationDiagnose a unit mismatch between the data and the value of R in an ideal-gas calculation.

Interprete as evidências 4

The simple and combined gas laws

  • Volume–temperature lines that meet at one pointInterpret the common intercept of volume–temperature plots for gases as absolute zero.

Pressure and its measurement

  • Read a closed-end manometerFind a gas pressure from a closed-end manometer and recognise that atmospheric pressure does not enter.
  • Read an open-end manometerFind a gas pressure from an open-end manometer when the mercury is lower on the gas side.

Gas density and molar mass

  • Identify a gas from its densityIdentify an unknown gas by comparing the molar mass calculated from its density with candidate gases.

Trabalhe de trás para frente 4

Gas stoichiometry

  • Sodium azide for an airbagCalculate the mass of a solid reactant needed to fill a given volume with gas at a stated pressure and temperature.
  • Which metal produced the hydrogen?Identify a metal from the volume of hydrogen it releases by working back to its molar mass.
  • How much limestone gives 1.50 L of CO₂?Work backwards from a measured gas volume to the mass of solid reactant required.

Gas density and molar mass

  • Molecular formula from gas densityCombine an empirical formula with a molar mass from gas density to find a molecular formula.

Planeje uma síntese 1

  • Pick a gas syringe big enoughPlan the size of gas-collection apparatus from the predicted volume of gas a reaction produces.

Explique por quê 2

Gas density and molar mass

  • Why does a hot-air balloon rise?Explain the buoyancy of heated air with the relation d = PM/RT.
  • Is humid air heavier or lighter than dry air?Explain why humid air is less dense than dry air at the same temperature and pressure.

Travou em leis dos gases e estequiometria de gases? Escaneie o problema.

Tire uma foto da reação da sua lista ou do livro e desenhe o mecanismo com cada seta corrigida. 1 scan grátis agora, sem cadastro; mais 1 com uma conta gratuita.

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