Conservation of Mass & Relative Formula Mass

Conservation of mass

• The law of conservation of mass: no atoms are lost or made in a chemical reaction, so the mass of the products equals the mass of the reactants
• This is why symbol equations must balance: the same number of atoms of each element on both sides
• Two kinds of number in an equation:
  • A multiplier in normal script before a formula, $2\text{H}_2\text{O}$, means two of the whole formula
  • A subscript inside a formula, $\text{H}_2\text{O}$, means two of that atom in one unit
• $2\text{Mg} + \text{O}_2 \rightarrow 2\text{MgO}$: 2 Mg and 2 O on each side

Relative formula mass

• The relative formula mass, $M_r$, of a compound is the sum of the relative atomic masses of all the atoms in the formula
• Worked example: $\text{Ca(OH)}_2$ has $A_r$ values Ca 40, O 16, H 1, so $M_r = 40 + 2 \times (16 + 1) = 74$
• In a balanced equation, the total $M_r$ of the reactants (in the amounts shown) equals the total $M_r$ of the products
• Percentage by mass of an element in a compound:

$$\text{\% by mass} = \frac{A_r \times \text{number of atoms of the element}}{M_r} \times 100$$

• Worked example: nitrogen in ammonium nitrate, $\text{NH}_4\text{NO}_3$ ($M_r = 80$). Two nitrogen atoms: $\frac{2 \times 14}{80} \times 100 = 35\%$

Mass changes when a gas is involved

• Some reactions appear to change mass. It is always because a reactant or product is a gas whose mass was not weighed
• Mass appears to increase when a metal reacts with oxygen: the oxygen came from the air and is now part of the solid oxide. $2\text{Mg} + \text{O}_2 \rightarrow 2\text{MgO}$
• Mass appears to decrease in a thermal decomposition: the carbon dioxide escapes into the air. $\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2$
• In terms of the particle model: gas particles are far apart and spread out, so they leave the open container (or are added from the air) without being weighed. In a closed system nothing escapes and the mass does not change

Chemical measurements and uncertainty

• Every measurement has some uncertainty
• Repeat a measurement and take the mean. The range of the results about the mean is a measure of the uncertainty:

$$\text{uncertainty} = \pm \frac{\text{range}}{2}$$

• Worked example: temperature rises of 12.0, 12.4 and 12.2 °C. Mean 12.2 °C, range 0.4 °C, so the result is $12.2 \pm 0.2$ °C
• An anomalous result, far from the others, is left out before the mean is taken
• Results are concordant when they are close together, for example titration volumes within 0.10 cm³