Chemistry · Chemical reactions · Grade 8

Rate of reaction and catalyst

Why does chalk powder “fizz” faster than a lump, and why does food spoil slowly in a fridge?

The situation

In the chemistry room, the teacher drew a large X on paper under three beakers: after acid is poured in, the solution turns cloudy and the X disappears — but at a different time in each beaker. It is the same at home: meat keeps for a long time in the fridge, milk sours quickly in the heat, hydrogen peroxide foams up on a wound, and chalk powder “boils” in acid faster than a lump does. What does the rate of a reaction depend on, and how can it be measured, increased or slowed down?

Topic

Rate of chemical reactions and catalysts. Chalk and hydrochloric acid: powder “boils” faster than a lump; sugar dissolves quickly in hot tea; catalase makes hydrogen peroxide froth on a wound

Key ideas

Factors affecting rate
Van 't Hoff rule
Catalyst

Formulas

v = \pm \frac{Δ c}{Δ t}

Rate of reaction — the change in concentration per unit time, mol/(L·s).

v = k {[A]}^{a} {[B]}^{b}

Law of mass action (Guldberg and Waage): $k$ is the rate constant; the exponents are found by experiment.

\frac{v_{2}}{v_{1}} = γ^{(t_{2} - t_{1}) / 10}

Van 't Hoff's rule: for every 10 °C rise in temperature the rate increases by a factor γ = 2–4.

k = A e^{- E_{a} / R T}

Arrhenius equation: $k$ is large if the activation energy $E_{a}$ is small or the temperature is high.

2 H_{2} O_{2} \overset{\overset{}{MnO_{2}}}{\to} 2 H_{2} O + O_{2} ↑

Catalytic decomposition: MnO₂ speeds up the reaction and remains unchanged itself.

Theory

Rate of reaction and collisions

Rate of reaction is the change in concentration per unit time of a substance that reacts or is formed: $v = \pm Δ c / Δ t$ , with units of mol/(L·s). For example, if the concentration of substance A falls from 0.6 to 0.4 mol/L in 10 s, v = 0.2 : 10 = 0.02 mol/(L·s). If a reaction takes place in one phase (a solution, a mixture of gases), it is homogeneous; if it takes place at the boundary between phases (solid chalk and acid), it is heterogeneous. Collision theory: for particles to react they must collide, and the collision must have enough energy (greater than the activation energy $E_{a}$ ) and the right orientation. Concentration, temperature, surface area and a catalyst all change the number of effective collisions (visible in the “Molecules” window).

Concentration and pressure: the law of mass action

Guldberg and Waage (1864–1867): at constant temperature, the rate is proportional to the product of the concentrations of the reacting substances: $v = k {[A]}^{a} {[B]}^{b}$ , where $k$ is the rate constant. For some reactions the exponents turn out to equal the coefficients (determined by experiment): $v = k [H_{2}] [I_{2}]$ for $H_{2} + I_{2} \overset{}{\to} 2 HI$ , $v = k {[NO]}^{2} [O_{2}]$ for $2 NO + O_{2} \overset{}{\to} 2 NO_{2}$ ; for complex reactions they are found by experiment. The concentration of a solid does not appear in the expression — its surface is what matters. In gases, if the pressure rises (the volume falls), the concentrations increase: if the volume is halved, the reaction of NO with O₂ speeds up 2²·2 = 8 times. In our experiment the acid in $Na_{2} S_{2} O_{3} + H_{2} SO_{4} \overset{}{\to} Na_{2} SO_{4} + S ↓ + SO_{2} ↑ + H_{2} O$ is in excess: the time for X to disappear is inversely proportional to the thiosulfate concentration, so the rate is proportional to $c (Na_{2} S_{2} O_{3})$ .

Temperature: van 't Hoff's rule

When the temperature rises by 10 °C, the rate of most reactions increases 2–4 times: $v_{2} / v_{1} = γ^{(t_{2} - t_{1}) / 10}$ , where $γ$ is the temperature coefficient (van 't Hoff, 1884). The reason is not just that molecules move faster: the fraction of molecules with energy greater than $E_{a}$ increases sharply. A more accurate law is the Arrhenius equation $k = A e^{- E_{a} / R T}$ . That is why food in the fridge (+4 °C) spoils several times more slowly than at room temperature, and milk sours quickly in the heat. Problem: if γ = 3 and the temperature rises from 20 °C to 50 °C, then $v_{2} / v_{1} = 3^{3} = 27$ times.

Surface area

A heterogeneous reaction takes place only at the phase boundary, so it speeds up when the substance is crushed. If 1 g of chalk is a single sphere (r ≈ 4.4 mm), its surface is ≈ 2.5 cm²; split into 8 pieces, it is 2 times larger; in a powder with grains of radius 0.2 mm it is ≈ 55 cm², that is 22 times larger. $CaCO_{3} + 2 HCl \overset{}{\to} CaCl_{2} + CO_{2} ↑ + H_{2} O$ : the flask gets lighter as CO₂ escapes, and 1.00 g of CaCO₃ gives 0.44 g of CO₂. That is why a thin stick burns faster than a thick log, and flour, sugar and coal dust can explode in air — dust must never be allowed to build up in mills and mines.

Catalyst and inhibitor

A catalyst speeds up a reaction while remaining unchanged itself at the end: it takes the reaction along a different path with a lower activation energy. In the decomposition of H₂O₂, $E_{a}$ ≈ 75 kJ/mol; with MnO₂ it is ≈ 58 kJ/mol, and with liver catalase ≈ 23 kJ/mol (8–14 kJ/mol in other measurements). A catalyst changes neither the heat of reaction nor the equilibrium. In homogeneous catalysis the catalyst is in the same phase as the reactants; in heterogeneous catalysis it is on a solid surface: MnO₂, iron in industry (ammonia synthesis), V₂O₅ (sulfuric acid), Pt–Rh gauze (nitric acid), a car's catalytic converter. Enzymes are biological catalysts: catalase in cells breaks down toxic H₂O₂; on boiling, the protein structure is destroyed and the enzyme stops working. An inhibitor slows a reaction down: a stabiliser is added to the hydrogen peroxide sold in pharmacies, corrosion inhibitors to metals, and antioxidants to fats.

Laboratory, safety and the model

Experiment on the factors affecting rate (Grade 8 §33, Grade 11 §23): 1) Na₂S₂O₃ solution and water in different volumes (30 mL in total) are poured into three beakers and placed on paper with an X drawn on it; the time from adding 10 mL of H₂SO₄ until the X disappears is measured, $v \approx Δ c (S) / t$ ; 2) the same experiment in water baths at different temperatures; 3) a lump and a powder of chalk in acid (on a balance); 4) MnO₂ and potato added to H₂O₂. Safety: safety goggles; acids burn the skin; the thiosulfate reaction releases SO₂, which has a sharp smell — ventilate the room or work in a fume cupboard; only 3 % H₂O₂ is used in school. Model: the rate of the thiosulfate reaction is taken to be proportional to $c (Na_{2} S_{2} O_{3})$ with $E_{a}$ = 50 kJ/mol (γ ≈ 2.0) — the real mechanism is complex; the X disappears when the sulfur reaches 1 mmol/L; the chalk pieces are spherical (ρ = 2.71 g/cm³) and the CO₂ escapes at once; the decomposition of H₂O₂ is first order, the rate constants are schematic, and the enzyme is destroyed above 50 °C (schematic); the “Molecules” window is schematic — sizes and speeds are not to scale.

Did you know?

The Dutch chemist Jacobus van 't Hoff described the effect of temperature on reaction rate in 1884 in his book “Studies in Chemical Dynamics”. In 1901 he received the first Nobel Prize in Chemistry.
Catalase is one of the fastest enzymes: a single molecule breaks down millions of H₂O₂ molecules into water and oxygen every second. It is found in almost all organisms that live in an oxygen-containing environment.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

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Reversible reactions and equilibrium — Grade 8
Chemical industry and plants — Grade 9