2.6.4 Reacting masses and concentration in g dm⁻³

A balanced equation fixes the ratio in which substances react

Definition

Relative formula mass

The sum of the relative atomic masses of all the atoms shown in the formula of a substance, given the symbol Mr.

The numbers written in front of the formulae are the coefficients, and they give the ratio in which the substances react.
The subscripts inside a formula count atoms, and are never used as the reacting ratio.
Turning that ratio into masses takes the relative formula mass of each substance.
Multiply each coefficient by that substance's $M_r$ to get the mass ratio the equation predicts.
For $CaCO3→CaO+CO2\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2$ the mass ratio is $100 : 56 : 44$ .
Those figures balance, because $56 + 44 = 100$ and mass is conserved.

Key Idea

Coefficients give a ratio of amounts, which becomes a ratio of masses once each $M_r$ is applied.
The mass ratio scales, so doubling one mass doubles every other mass in the equation.

Scaling the mass ratio to the masses in the question

Write the balanced equation, and write the mass ratio underneath it.
Find the scale factor by dividing the mass given in the question by the ratio mass for that same substance.
Multiply every other mass in the ratio by that scale factor.
For $g25.0\ \text{g}$ of $CaCO3\text{CaCO}_3$ against a ratio mass of $100$ : $factor=25.0100=0.250\text{scale factor} = \frac{25.0}{100} = 0.250$
The mass of $CaO\text{CaO}$ is then the ratio mass of $56$ scaled by the same factor: $gm(\text{CaO}) = 0.250 \times 56 = 14.0\ \text{g}$
The answer is smaller than the starting mass because carbon dioxide is given off as well.

Note

One scale factor runs the whole calculation, because it is the same for every substance in the equation.
The total mass of the products cannot exceed the total mass of the reactants, though a single product may well outweigh the one reactant named in the question.

Concentration in grams per cubic decimetre

Definition

Concentration

The mass or amount of a solute dissolved in a given volume of solution.

A solution's concentration compares the mass of solute with the volume of solution it is dissolved in.
The calculation is: $\frac{m}{V}$
Here $c$ is in $dm−3\text{g dm}^{-3}$ , $m$ is in $g\text{g}$ and $V$ is in $dm3\text{dm}^3$ .
Volumes are usually measured in $cm3\text{cm}^3$ , and $cm31\ \text{dm}^3 = 1000\ \text{cm}^3$ .
So $cm3250\ \text{cm}^3$ becomes $250 \div 1000 = 0.250\ \text{dm}^3$ .
Dissolving $g5.0\ \text{g}$ of sodium chloride to make that volume of solution gives: $\frac{5.0}{0.250} = 20.0\ \text{g dm}^{-3}$

Common Mistake

Convert the volume first, because dividing by a volume in $cm3\text{cm}^3$ gives a number a thousand times too small.
The volume is that of the finished solution, not the volume of water that was added.

Checking a mass or a concentration

Check the equation is balanced before taking any ratio from it.
Check every mass is in grams and every volume is in $dm3\text{dm}^3$ .
Check the total mass of the products does not exceed the total mass of the reactants.
Keep extra figures through the working and round once, at the end.
Check the unit on the final answer: $g\text{g}$ for a mass and $dm−3\text{g dm}^{-3}$ for a concentration.

Self review

What do the coefficients in a balanced equation tell you?
How is a balanced equation turned into a ratio of masses?
What mass of calcium oxide forms when $g25.0\ \text{g}$ of calcium carbonate decomposes?
How many cubic decimetres is $cm3250\ \text{cm}^3$ ?
What is the concentration when $g5.0\ \text{g}$ of solute makes $cm3250\ \text{cm}^3$ of solution?

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A balanced equation shows the ratio in which substances react. The numbers in front of formulae are coefficients, while subscripts inside formulae only count atoms and are not used as the reacting ratio.

For $CaCO3→CaO+CO2\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2$ , the relative formula masses are $100$ , $56$ , and $44$ . Applying these values to the coefficients gives the mass ratio:

\text{CaCO}_3 : \text{CaO} : \text{CO}_2 = 100 : 56 : 44

The ratio balances because $56 + 44 = 100$ , showing conservation of mass.

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What do the coefficients in a balanced equation tell you?

2.6.4 Reacting masses and concentration in g dm⁻³

A balanced equation fixes the ratio in which substances react

Definition

Relative formula mass

The sum of the relative atomic masses of all the atoms shown in the formula of a substance, given the symbol Mr.

The numbers written in front of the formulae are the coefficients, and they give the ratio in which the substances react.
The subscripts inside a formula count atoms, and are never used as the reacting ratio.
Turning that ratio into masses takes the relative formula mass of each substance.
Multiply each coefficient by that substance's $M_r$ to get the mass ratio the equation predicts.
For $CaCO3→CaO+CO2\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2$ the mass ratio is $100 : 56 : 44$ .
Those figures balance, because $56 + 44 = 100$ and mass is conserved.

Key Idea

Coefficients give a ratio of amounts, which becomes a ratio of masses once each $M_r$ is applied.
The mass ratio scales, so doubling one mass doubles every other mass in the equation.

Scaling the mass ratio to the masses in the question

Write the balanced equation, and write the mass ratio underneath it.
Find the scale factor by dividing the mass given in the question by the ratio mass for that same substance.
Multiply every other mass in the ratio by that scale factor.
For $g25.0\ \text{g}$ of $CaCO3\text{CaCO}_3$ against a ratio mass of $100$ : $factor=25.0100=0.250\text{scale factor} = \frac{25.0}{100} = 0.250$
The mass of $CaO\text{CaO}$ is then the ratio mass of $56$ scaled by the same factor: $gm(\text{CaO}) = 0.250 \times 56 = 14.0\ \text{g}$
The answer is smaller than the starting mass because carbon dioxide is given off as well.

Note

One scale factor runs the whole calculation, because it is the same for every substance in the equation.
The total mass of the products cannot exceed the total mass of the reactants, though a single product may well outweigh the one reactant named in the question.

Concentration in grams per cubic decimetre

Definition

Concentration

The mass or amount of a solute dissolved in a given volume of solution.

A solution's concentration compares the mass of solute with the volume of solution it is dissolved in.
The calculation is: $\frac{m}{V}$
Here $c$ is in $dm−3\text{g dm}^{-3}$ , $m$ is in $g\text{g}$ and $V$ is in $dm3\text{dm}^3$ .
Volumes are usually measured in $cm3\text{cm}^3$ , and $cm31\ \text{dm}^3 = 1000\ \text{cm}^3$ .
So $cm3250\ \text{cm}^3$ becomes $250 \div 1000 = 0.250\ \text{dm}^3$ .
Dissolving $g5.0\ \text{g}$ of sodium chloride to make that volume of solution gives: $\frac{5.0}{0.250} = 20.0\ \text{g dm}^{-3}$

Common Mistake

Convert the volume first, because dividing by a volume in $cm3\text{cm}^3$ gives a number a thousand times too small.
The volume is that of the finished solution, not the volume of water that was added.

Checking a mass or a concentration

Check the equation is balanced before taking any ratio from it.
Check every mass is in grams and every volume is in $dm3\text{dm}^3$ .
Check the total mass of the products does not exceed the total mass of the reactants.
Keep extra figures through the working and round once, at the end.
Check the unit on the final answer: $g\text{g}$ for a mass and $dm−3\text{g dm}^{-3}$ for a concentration.

Self review

What do the coefficients in a balanced equation tell you?
How is a balanced equation turned into a ratio of masses?
What mass of calcium oxide forms when $g25.0\ \text{g}$ of calcium carbonate decomposes?
How many cubic decimetres is $cm3250\ \text{cm}^3$ ?
What is the concentration when $g5.0\ \text{g}$ of solute makes $cm3250\ \text{cm}^3$ of solution?

Previous Next

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Teach Genie

Review 2.6.4 Reacting masses and concentration in g dm⁻³ by teaching Genie

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7 minute activity

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For $CaCO3→CaO+CO2\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2$ , the relative formula masses are $100$ , $56$ , and $44$ . Applying these values to the coefficients gives the mass ratio:

\text{CaCO}_3 : \text{CaO} : \text{CO}_2 = 100 : 56 : 44

The ratio balances because $56 + 44 = 100$ , showing conservation of mass.

Flashcards

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29 flashcards

Practice flashcards

What do the coefficients in a balanced equation tell you?

2.6.4 Reacting masses and concentration in g dm⁻³

A balanced equation fixes the ratio in which substances react

Scaling the mass ratio to the masses in the question

Concentration in grams per cubic decimetre

Checking a mass or a concentration

Review 2.6.4 Reacting masses and concentration in g dm⁻³ by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

2.6.4 Reacting masses and concentration in g dm⁻³ Revision Guide

2.6.4 Reacting masses and concentration in g dm⁻³

A balanced equation fixes the ratio in which substances react

Scaling the mass ratio to the masses in the question

Concentration in grams per cubic decimetre

Checking a mass or a concentration

Review 2.6.4 Reacting masses and concentration in g dm⁻³ by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

2.6.4 Reacting masses and concentration in g dm⁻³ Revision Guide