Stoichiometry - Chemistry

1. Fundamental Concepts

Mole: The central unit of stoichiometry. 1 mole = $6.022 \times 10^{23}$ particles (Avogadro's Number, $N_A$).

Molar Mass ($M$): The mass of one mole of a substance (g/mol). Numerically equal to the atomic or formula mass from the Periodic Table.

Avogadro's Law: Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

STP (Standard Temperature and Pressure): $0^\circ\text{C}$ ($273\text{ K}$) and $1\text{ atm}$. At STP, 1 mole of any ideal gas occupies 22.4 L.

Molarity ($M$): Concentration measured as moles of solute per liter of solution ($M = n/V$).

2. Key Concepts

Balanced Chemical Equations: Must be balanced first to determine the quantitative relationship between reactants and products.

Mole Ratio: Derived from the coefficients in a balanced equation.

Example: In $2\text{H}_2(g) + \text{O}_2(g) \rightarrow 2\text{H}_2\text{O}(l)$, the ratio of $\text{H}_2$ to $\text{H}_2\text{O}$ is $2:2$ (or $1:1$).

Limiting Reactant: The reactant that is completely consumed first. It limits the amount of product formed.

Excess Reactant: The reactant that remains after the reaction is complete.

Theoretical Yield: The maximum amount of product that can be formed, calculated from the limiting reactant.

Percent Yield: A measure of reaction efficiency.

Formula: $\frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100\%$.

3. Examples

Easy

Question: How many moles are present in $88.0\text{ g}$ of Carbon Dioxide ($\text{CO}_2$)?

Solution:

1. Calculate Molar Mass: $12.0 + (2 \times 16.0) = 44.0\text{ g/mol}$.

2. Convert to Moles:

$$ \text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{88.0\text{ g}}{44.0\text{ g/mol}} = 2.00\text{ mol} $$

Medium

Question: Given the balanced equation $\text{N}_2(g) + 3\text{H}_2(g) \rightarrow 2\text{NH}_3(g)$, what mass of $\text{NH}_3$ (Ammonia) is produced when $6.0\text{ mol}$ of $\text{H}_2$ reacts completely?

Solution:

1. Apply Mole Ratio: $\frac{2\text{ mol NH}_3}{3\text{ mol H}_2}$.

2. Find Moles of Product:

$$ 6.0\text{ mol H}_2 \times \frac{2\text{ mol NH}_3}{3\text{ mol H}_2} = 4.0\text{ mol NH}_3 $$

3. Convert to Grams: (Molar Mass of $\text{NH}_3 = 17.0\text{ g/mol}$)

$$ 4.0\text{ mol} \times 17.0\text{ g/mol} = 68\text{ g} $$

Hard (Limiting Reactant & Percent Yield)

Question: $10.0\text{ g}$ of $\text{H}_2$ is mixed with $90.0\text{ g}$ of $\text{O}_2$ and ignited to produce water ($2\text{H}_2(g) + \text{O}_2(g) \rightarrow 2\text{H}_2\text{O}(l)$). If $85.0\text{ g}$ of water is actually collected, what is the percent yield?

Solution:

1. Identify Limiting Reactant:

$\text{H}_2$: $10.0\text{ g} / 2.0\text{ g/mol} = 5.0\text{ mol}$.

$\text{O}_2$: $90.0\text{ g} / 32.0\text{ g/mol} = 2.8125\text{ mol}$.

Check Requirement: To react with $5.0\text{ mol H}_2$, we need $2.5\text{ mol O}_2$ (since ratio is $2:1$). We have $2.8125\text{ mol O}_2$, which is enough.

Conclusion: $\text{H}_2$ is the Limiting Reactant.

2. Calculate Theoretical Yield:

Ratio of $\text{H}_2$ to $\text{H}_2\text{O}$ is $1:1$. So, $5.0\text{ mol}$ of $\text{H}_2\text{O}$ are formed.

Mass = $5.0\text{ mol} \times 18.0\text{ g/mol} = 90.0\text{ g}$.

3. Calculate Percent Yield: $$ \frac{85.0\text{ g}}{90.0\text{ g}} \times 100\% = 94.4\% $$

4. Problem-Solving Techniques

The Mole Map:

Convert all given quantities (grams, liters, particles) to Moles first.

Use the Mole Ratio (from the balanced equation) to switch between different substances.

Convert back to the desired unit (grams, liters, etc.).

Mantra: Grams $\leftrightarrow$ Moles $\leftrightarrow$ Moles $\leftrightarrow$ Grams.

Limiting Reactant Strategy:

When given amounts for two reactants, calculate the yield for each reactant separately.

The reactant that produces the smaller amount of product is the Limiting Reactant. That smaller amount is the Theoretical Yield.

Dimensional Analysis:

Always carry units through the calculation.

Ensure units cancel out correctly (e.g., mol in the numerator cancels mol in the denominator). This is the fastest way to check if your setup is correct.

Significant Figures: Pay close attention to significant figures, especially when adding/multiplying. The final answer should reflect the precision of the given data.