Higher Tier: derive balancing numbers from reacting masses
| English | 中文 | Pinyin |
|---|---|---|
| reacting mass | 反应质量 | fǎn yìng zhì liàng |
| balancing number | 配平系数 | pèi píng xì shù |
What would explain this observation?
- Higher Tier: A reaction’s measured masses may be in a ratio such as 2.4:1.6:4.0, while its equation coefficients are 2:1:2. Converting masses to amounts reveals the correct ratio.
- Start with a prediction. State the quantities or features you would compare, then decide what evidence could distinguish two explanations.
Build the model
- For known substance formulae, divide each reacting mass 反应质量 by its molar mass to obtain amounts. Divide all amounts by the smallest one, then multiply the entire ratio if needed to obtain small whole numbers. Use those numbers as coefficients before the supplied formulae. Never change the formulae themselves just to make the ratio look simpler.
- balancing number 配平系数: A whole-number coefficient before a formula in a balanced equation; reacting mass: The mass actually consumed or formed in the stated reaction.
What should be done with a ratio 2:1.5:1?
For Mg, O₂ and MgO with molar masses 24, 32 and 40 g per mol, supplied masses 2.4, 1.6 and 4.0 g give 0.10, 0.050 and 0.10 mol. Dividing by 0.050 gives 2:1:2, hence 2Mg + O₂ → 2MgO. The oxygen formula is O₂, so its molar mass is 32, not the atomic value 16.
Match each technical term to its precise meaning.
Use the definitions to distinguish related quantities and processes.
Choose evidence that can test it
- For Mg, O₂ and MgO with molar masses 24, 32 and 40 $\dfrac{\text{g}}{\text{mol}}$, supplied masses 2.4, 1.6 and 4.0 g give 0.10, 0.050 and 0.10 mol. Dividing by 0.050 gives 2:1:2, hence 2Mg + O₂ → 2MgO. The oxygen formula is O₂, so its molar mass is 32, not the atomic value 16.
- Organise substance, mass, molar mass, amount and simplified ratio in a table. When a ratio includes 1.5, multiply every term by two instead of rounding that term to one or two. Check the resulting atom counts and conserved total mass. Reacting masses must exclude unreacted excess or unrelated apparatus; otherwise they cannot directly establish the equation ratio.
Which two habits make the investigation or model in this case more defensible?
Organise substance, mass, molar mass, amount and simplified ratio in a table. When a ratio includes 1.5, multiply every term by two instead of rounding that term to one or two. Check the resulting atom counts and conserved total mass. Reacting masses must exclude unreacted excess or unrelated apparatus; otherwise they cannot directly establish the equation ratio.
Work from known quantities
- State the known values and their units. Choose the relation because its assumptions fit this case, then rearrange before substitution.
- Known: masses 5.4 g Al, 4.8 g O₂ and 10.2 g Al₂O₃ give amounts 0.20, 0.15 and 0.10 mol using molar masses 27, 32 and 102. Ratio=2:1.5:1, so multiply all terms by two to obtain 4:3:2. The equation 4Al + 3O₂ → 2Al₂O₃ conserves four Al and six O atoms.
Amounts Al:O₂:Al₂O₃ are 0.4:0.3:0.2 mol. After finding the smallest whole-number ratio, give the O₂ coefficient. Use the same sequence: known quantities → model → relation → substitution → unit and interpretation.
Amounts Al:O₂:Al₂O₃ are 0.4:0.3:0.2 mol. After finding the smallest whole-number ratio, give the O₂ coefficient.
The result is 3 . Known: masses 5.4 g Al, 4.8 g O₂ and 10.2 g Al₂O₃ give amounts 0.20, 0.15 and 0.10 mol using molar masses 27, 32 and 102. Ratio=2:1.5:1, so multiply all terms by two to obtain 4:3:2. The equation 4Al + 3O₂ → 2Al₂O₃ conserves four Al and six O atoms.
Check the conclusion and its limits
- Whole-number coefficients are an equation ratio, not a demand to round every experimental amount independently. A product may contain a bracketed formula whose full molar mass must be calculated. Rearranging n=m/M gives M=m/n, but a derived M still needs the correct substance identity to interpret it.
- Return to the original observation. Explain what the result supports, which conditions it assumes, and one way to test a competing explanation.
Reacting mass ratios can be used as coefficients without converting to moles. This claim is false: Whole-number coefficients are an equation ratio, not a demand to round every experimental amount independently. A product may contain a bracketed formula whose full molar mass must be calculated. Rearranging n=m/M gives M=m/n, but a derived M still needs the correct substance identity to interpret it.
Higher Tier: derive balancing numbers from reacting masses: For Mg, O₂ and MgO with molar masses 24, 32 and 40 $\dfrac{\text{g}}{\text{mol}}$, supplied masses 2.4, 1.6 and 4.0 g give 0.10, 0.050 and 0.10 mol. Dividing by 0.050 gives 2:1:2, hence 2Mg + O₂ → 2MgO. The oxygen formula is O₂, so its molar mass is 32, not the atomic value 16.
Reacting mass ratios can be used as coefficients without converting to moles.
Whole-number coefficients are an equation ratio, not a demand to round every experimental amount independently. A product may contain a bracketed formula whose full molar mass must be calculated. Rearranging n=m/M gives M=m/n, but a derived M still needs the correct substance identity to interpret it.
A whole-number coefficient before a formula in a balanced equation: write the technical term.
balancing number means A whole-number coefficient before a formula in a balanced equation.