Calculating Rates of Reaction

Mean rate of reaction

• The rate of a reaction is found by measuring how much reactant is used or how much product is formed in a given time

$$\text{mean rate} = \frac{\text{quantity of reactant used}}{\text{time taken}} \qquad \text{mean rate} = \frac{\text{quantity of product formed}}{\text{time taken}}$$

• The quantity is a mass in g or a volume in cm³, so the units of rate are g/s or cm³/s
• (HT) The quantity can also be in moles, giving a rate in mol/s
• Worked example: 48 cm³ of hydrogen is collected in 60 s, so the mean rate is $\frac{48}{60} = 0.80$ cm³/s
• Worked example (HT): 0.0048 mol of gas in 60 s: $8.0 \times 10^{-5}$ mol/s

Rate graphs

• A graph of product formed against time starts steep and levels off: the reaction is fastest at the start, slows as the reactants are used up, and stops when one reactant runs out
• The steeper the line, the faster the rate. When the line is flat the reaction has finished
• A graph of reactant remaining against time falls steeply and then flattens

Rate at a particular time

• The rate at one moment is the gradient of the curve at that point. Draw a tangent, a straight line that just touches the curve there, and find its slope
• (HT) Gradient of the tangent:

$$\text{rate} = \frac{\text{change in } y}{\text{change in } x}$$

• Worked example (HT): a tangent at 45 s passes through (20 s, 10 cm³) and (70 s, 60 cm³). Rate $= \frac{60 - 10}{70 - 20} = \frac{50}{50} = 1.0$ cm³/s
• Use a large triangle on the tangent, so small reading errors matter less