Mass and Gaseous Volume Relationships in Chemical Reactions
Calculate theoretical yields from chemical equations
A balanced equation establishes the connection between the mass (or moles) of a known substance to the mass (or moles) of an unknown substance.
For example:
Calculations like this can be done in the following steps:
Determine the limiting reactant in excess when quantities of reacting substances are given
If there is more than one reactant, the limiting reactant needs to be identified. We determine the amount (in moles) of both reactants and use the molar ratio to from the equation to determine which will be completely consumed in the reaction and which is present in excess. The limiting reagent is the one used in the calculation.
Solve problems involving theoretical, experimental and percentage yield
The amount of product produced in an experiment is called the experimental yield. It is often significantly less than the theoretical yield. To express how successful the preparation of a product has been, you calculate the percentage yield.
Apply Avogadro’s law to calculate reacting volumes of gases
Avogadro’s law is that equal volumes of gases at the same temperature and pressure contain equal numbers of particles. It can be expressed mathematically as:
For example:
Apply the concept of molar volume at standard temperature and pressure in calculations
For example, if we have 1.00 mol of an ideal gas at 273K (0oC) and 1.0 atm (101.3 kPa). We can calculate the volume of the gas at these conditions using the ideal gas equation:
This is the molar volume (Vm) of the gas under the specified conditions.
A gas will always expand to fill any container, so it is pointless to specify a gas volume without specifying its temperature and pressure.
Standard temperature is 0 degree C
Standard pressure is 1 atm
These are often used when comparing gases.
Many chemical reactions involve gases. We can use these molar volumes (assuming ideal gas behaviour) to carry out stoichiometric calculations.
Solve problems involving the relationship between temperature, pressure and volume for a fixed mass of an ideal gas
When we use the ideal gas equation, we must ensure that the correct units are used; P in kPa, V in dm3 and T in K
The ideal gas equation defines the behaviour of an ideal gas. Most gases approach this behaviour at low pressures. We can therefore use this equation to determine one gas quantity (i.e. P) if the other three quantities are known (V, T and n).
Where:
P1 and P2 = the initial and final gas pressures V1 and V2 = the volumes
T1 and T2 = the temperatures n1 and n2 = the amounts of gas
We frequently deal with situations in which the amount of gas is fixed. For this fixed amount of gas, the ideal gas equation reduces to what is sometimes called the combined gas law or combined gas equation.
This equation can be used to solve for any of the six quantities if the other five are known. Remember when using this that the units for P1 and P2 must be the same, the units for V1 and V2 the same, and temperature must be measured on the Kelvin scale.
For example:
Solve problems using the ideal gas equation, PV = nRT
The constant R is the universal gas constant. The usual units are:
- P in kPa
- V in dm3
- T in K
- n in mol
Using these, R becomes 8.31 J K-1 mol-1
For example:
Analyse graphs relating to the ideal gas equation
Gas quantities, pressure, volume, amount of gas and temperature are related by a series of mathematical expression known as the gas laws.
Boyle’s Law
Boyle studied the relationship between pressure and volume and found that:
The pressure exerted by a given mass of gas at a constant temperature is inversely proportional to the volume occupied by the gas
This relationship can be represented in various ways. A plot of V versus P produces a hyperbola, indicating an inverse relationship. Plotting V verses 1/P produces a straight line with an intercept of zero.
This relationship can be represented by the equation:
k is a constant for a given sample of gas at a specified temperature. This can also be shown:
P1 = initial pressure
P2 = final pressure
V1 = initial volume
V2 = final volume
This relationship applies provided that the temperature and amount of gas remain constant. Boyle’s law is consistent with the kinetic molecular theory. If the volume of the container is increases, the particles travel greater distances between collisions with each other and the walls of the container. Fewer collisions with the walls mean decreased force per unit area and hence a decreased pressure.
The kinetic molecular theory applies to an ideal gas. In an ideal gas the particles are completely independent. Real gases behave less ideally when the pressure is high. Thus, real gases show some deviation from Boyle’s law at high pressures. PV is not quite as constant as the pressure increases to values much higher that atmospheric pressure.
For example: