# Stoichiometric relationships

Physics I · Chemistry · https://tryals.app/learn/physics-i/stoichiometric-relationships

## Stoichiometric Foundations

**Stoichiometry** is the quantitative backbone of chemistry, linking the amounts of reactants consumed to products formed via **mole ratios**.

In a **balanced equation** ($aA + bB \longrightarrow cC + dD$), the coefficients $a, b, c, d$ are the **stoichiometric coefficients**. Mass and charge must always be conserved.

$$\text{grams} \;\xrightarrow{\div\,M}\; \text{moles} \;\xrightarrow{\times\,\text{ratio}}\; \text{moles of target} \;\xrightarrow{\times\,M}\; \text{grams}$$

**Common pitfall:** Balanced coefficients relate **moles**, never grams. Converting masses to moles before using the ratio is the non-negotiable detour of every stoichiometry problem.

**Limiting reagent**: The reactant that runs out first and determines the maximum yield. To find it, convert all reactants to moles and compare to the required ratio.

## Yield and Concentration

**Percent yield** measures efficiency: $\%\;\text{yield} = \frac{\text{actual yield}}{\text{theoretical yield}}\times 100$.

| Measure | Formula |
| --- | --- |
| **Molarity** $M$ | $\frac{n_{\text{solute}}}{V_{\text{solution}}}$ |
| **Mole fraction** $x_i$ | $\frac{n_i}{\sum n_j}$ |
| **Molality** $m$ | $\frac{n_{\text{solute}}}{m_{\text{solvent (kg)}}}$ |

Here $n$ is moles, $V$ is volume in liters, and $m_{\text{solvent}}$ is mass in kilograms.

**Tip:** Dimensional analysis is your best friend. Track units through every step and cancel them; if the units come out wrong, the calculation is wrong.

## Practice questions

5 of this lesson's 13 practice questions, with answers. The full set is in the app.

### 1. Order the steps to balance a chemical equation by inspection.

**Answer:**

1. Write the unbalanced equation with correct formulas for all species
2. Count atoms of each element on both sides of the arrow
3. Adjust stoichiometric coefficients (never subscripts) to equalise atom counts
4. Verify that total atom counts and any net charge match on both sides

**Why:** Only coefficients may be changed when balancing. Changing subscripts would alter the chemical identity of the compounds.

Page: https://tryals.app/practice/physics-i/stoichiometric-relationships/order-the-steps-to-balance-a-chemical-equation-by-inspection

### 2. For the reaction $2H_{2} + O_{2} \to 2H_{2}O$, you mix **4 mol** of $H_2$ with **1 mol** of $O_2$. What limits the water you can make?

A. The hydrogen, there is more of it, so it dominates
B. Nothing, all 5 mol of gas become water
C. The oxygen, leaving 2 mol of H₂ unused
D. The reaction stops at 1 mol of water

**Answer:** C. The oxygen, leaving 2 mol of H₂ unused

**Why:** Stoichiometry is recipe arithmetic: 1 mol O₂ supports exactly 2 mol H₂ → 2 mol H₂O, stranding the excess hydrogen. The scarcer-in-ratio ingredient (the limiting reagent) fixes the yield, like running out of cheese with bread to spare.

Page: https://tryals.app/practice/physics-i/stoichiometric-relationships/for-the-reaction-2h2-o2-2h2o-you-mix-4-mol-of-h2-with-1-mol-of

### 3. Propane burns: $C_{3}H_{8} + 5O_{2} \to 3CO_{2} + 4H_{2}O$. How many moles of $O_2$ are needed to burn **2 mol** of propane completely?

**Answer:** 10 (within ±0.01)

**Why:** 2 × 5 = 10 mol of O₂. Balanced coefficients are exchange rates between substances, all stoichiometry is unit conversion through those ratios.

Page: https://tryals.app/practice/physics-i/stoichiometric-relationships/propane-burns-c3h8-5o2-3co2-4h2o-how-many-moles-of-o2-are

### 4. In a balanced chemical equation, the number of atoms of each element is the same on both sides.

**Answer:** True

**Why:** Conservation of mass requires atom counts to be equal on reactant and product sides. Coefficients are chosen to ensure this.

Page: https://tryals.app/practice/physics-i/stoichiometric-relationships/in-a-balanced-chemical-equation-the-number-of-atoms-of-each-element

### 5. A reaction runs out of one reactant while another remains. Why does the limiting reagent determine the yield rather than the total mass of reactants?

A. Because the limiting reagent is always the one with the smallest mass
B. Because the reaction rate depends only on the limiting reagent
C. Because reactions consume reactants in fixed MOLE ratios
D. Because excess reactant becomes an inert impurity that halts the reaction

**Answer:** C. Because reactions consume reactants in fixed MOLE ratios

**Why:** Stoichiometry counts particles. Extra frames do not become bicycles once the wheels run out, and mass is the wrong currency for the comparison.

Page: https://tryals.app/practice/physics-i/stoichiometric-relationships/a-reaction-runs-out-of-one-reactant-while-another-remains-why-does