Grade 10

Advanced

6 min

Lesson 6 of 12

Stoichiometric Ratios and Balancing

Not Started

Mastering the use of coefficients in balanced equations to understand the quantitative relationships between reactants.

How do rocket scientists ensure a spacecraft doesn't run out of fuel mid-flight or explode from an oxygen surplus? It all comes down to the perfect 'recipe' found in a balanced chemical equation.

Learning Objectives

1.Balance complex chemical equations including combustion and redox-style reactions
2.Interpret coefficients as molar ratios for stoichiometric calculations
3.Identify and prove the conservation of mass within a balanced chemical equation

The Law of the Scale

In chemistry, the Law of Conservation of Mass dictates that matter cannot be created or destroyed. This means every single atom that enters a reaction as a reactant must exit as a product. To represent this, we use coefficients—large numbers placed in front of chemical formulas. Unlike subscripts, which define the molecule's identity (like the 2 in $H_2O$ ), coefficients are multipliers that change the quantity without changing the substance. Balancing an equation is like solving a puzzle where both sides of the arrow must have an identical count of every element.

Balance the formation of water: $H_2 + O_2 \rightarrow H_2O$

1. Count atoms: Left has 2H, 2O. Right has 2H, 1O. 2. Add a coefficient to the right: $H_2 + O_2 \rightarrow 2H_2O$ . Now O is balanced (2), but H is not (4 on right). 3. Adjust the left: $2H_2 + O_2 \rightarrow 2H_2O$ . 4. Final check: 4H and 2O on both sides.

Quick Check

Why can we change coefficients but never subscripts when balancing an equation?

Think about the difference between having two bicycles and one tricycle.

Answer

Changing a subscript changes the identity of the substance (e.g., $H_2O$ is water, but $H_2O_2$ is hydrogen peroxide), whereas a coefficient only changes the amount.

The Combustion Strategy

Combustion reactions (burning hydrocarbons in oxygen) are notoriously tricky because oxygen appears in multiple products. To master these, use the CHO Method: Balance Carbon first, Hydrogen second, and Oxygen last. If you end up with a fraction for oxygen, such as $\frac{13}{2}$ , simply multiply the entire equation by 2 to clear it. This systematic approach prevents the 'infinite loop' where changing one coefficient breaks another.

Balance $C_3H_8 + O_2 \rightarrow CO_2 + H_2O$

1. Carbon: 3 on left, so add 3 to $CO_2$ . ( $C_3H_8 + O_2 \rightarrow 3CO_2 + H_2O$ ) 2. Hydrogen: 8 on left, so add 4 to $H_2O$ . ( $C_3H_8 + O_2 \rightarrow 3CO_2 + 4H_2O$ ) 3. Oxygen: Right side now has $(3 \times 2) + (4 \times 1) = 10$ atoms. Add 5 to $O_2$ . 4. Final: $C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O$ .

Quick Check

In the CHO method, why is Oxygen balanced last?

Look at which element stands alone.

Answer

Because oxygen often appears as a pure element ( $O_2$ ) on the reactant side, making it the easiest to adjust at the end without affecting other elements.

Coefficients as Molar Ratios

Once balanced, coefficients reveal the Stoichiometric Ratio. This is the 'bridge' that allows us to convert between different substances. In the equation $2H_2 + O_2 \rightarrow 2H_2O$ , the ratio of $H_2$ to $O_2$ is $2:1$ . This means for every 2 moles of Hydrogen gas, you must have 1 mole of Oxygen gas to react completely. These ratios are the fundamental units of chemical accounting, allowing us to predict yields and identify limiting reactants.

Balance the reaction between Copper and Nitric Acid: $Cu + HNO_3 \rightarrow Cu(NO_3)_2 + NO_2 + H_2O$

1. Note that Nitrogen appears in two products. Balance the $Cu$ first (1:1). 2. Look at the $NO_3$ groups. There are 2 in $Cu(NO_3)_2$ . 3. Try a coefficient of 4 for $HNO_3$ to account for the Nitrogen and Hydrogen: $Cu + 4HNO_3 \rightarrow Cu(NO_3)_2 + 2NO_2 + 2H_2O$ . 4. Check O: Left has $4 \times 3 = 12$ . Right has $6 + 4 + 2 = 12$ . Balanced!

Key Takeaways

1The Law of Conservation of Mass ensures that the total number of atoms of each element is equal on both sides of an equation.
2Coefficients are multipliers for the entire molecule; subscripts are specific to the atoms within the molecule.
3The CHO method (Carbon, Hydrogen, Oxygen) is the most efficient way to balance combustion reactions.
4Balanced coefficients represent the molar ratio, which serves as the conversion factor between reactants and products.

Quick Check

Multiple Choice

What is the coefficient of $O_2$ when the equation $C_2H_6 + O_2 \rightarrow CO_2 + H_2O$ is balanced with the smallest whole numbers?

Multiple Choice

In the balanced equation $N_2 + 3H_2 \rightarrow 2NH_3$ , what is the molar ratio of $H_2$ to $NH_3$ ?

True/False

Changing the subscripts in a chemical formula is an acceptable way to balance an equation if the coefficients become too large.

What's Next?

Review Tomorrow

In 24 hours, try to write down the CHO method steps and explain why we cannot change subscripts to a friend or family member.

Practice Activity

Find 5 unbalanced combustion reactions online and practice balancing them using the 'multiply by 2' trick for odd oxygen counts.

Browse

Browse

Stoichiometric Ratios and Balancing

Learning Objectives

The Law of the Scale

The Combustion Strategy

Coefficients as Molar Ratios

Key Takeaways

Quick Check

What's Next?

Stoichiometric Ratios and Balancing

Learning Objectives

The Law of the Scale

The Combustion Strategy

Coefficients as Molar Ratios

Key Takeaways

Quick Check

What's Next?