Problem 97 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

An amount of \(0.3 \mathrm{~mole}\) of \(\mathrm{SrCl}_{2}\) is mixed with \(0.2\) mole of \(\mathrm{K}_{3} \mathrm{PO}_{4}\). The maximum moles of \(\mathrm{KCl}\) which may form is (a) \(0.6\) (b) \(0.5\) (c) \(0.3\) (d) \(0.1\)

Step-by-Step Solution

Answer

0.6 moles of KCl.

Step 1: Write down the balanced chemical equation

Firstly, determine the balanced chemical equation for the reaction between \text{SrCl}_2 and \text{K}_3\text{PO}_4. The equation is:\[ \text{SrCl}_2 + \text{K}_3\text{PO}_4 \rightarrow \text{Sr}_3(\text{PO}_4)_2 + 3\text{KCl}. \]Notice that the reaction produces 3 moles of KCl for every mole of SrCl2 that reacts.

Step 2: Determine the limiting reactant

To find the limiting reactant, compare the mole ratio of the reactants with the coefficients in the balanced equation. For SrCl2, it reacts in a 1:1 ratio with K3PO4. You have 0.3 moles of SrCl2 and 0.2 moles of K3PO4, which means K3PO4 will limit the reaction because it is present in fewer moles than required by the stoichiometric ratios.

Step 3: Calculate the moles of KCl produced

As the reaction produces 3 moles of KCl for every mole of K3PO4 that reacts, and K3PO4 is the limiting reagent, you can calculate the moles of KCl produced by:\[ 0.2 \text{ moles of K}_3\text{PO}_4 \times \frac{3 \text{ moles of KCl}}{1 \text{ mole of K}_3\text{PO}_4} = 0.6 \text{ moles of KCl} \]Therefore, the maximum moles of KCl that can form is 0.6.

Key Concepts

Chemical Stoichiometry

Chemical stoichiometry is the field of chemistry that involves calculating the quantities of reactants and products in chemical reactions. It relies on the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. Thus, the amount of each element present in the reactants must be the same as that present in the products.

To make these calculations, chemists use balanced chemical equations, which provide the ratios in which reactants combine and products form. Understanding stoichiometry is essential for determining the proportions needed to create a product, how much of a reactant is necessary, or how much of a product can be created from given amounts of reactants.

Importance of Mole Ratios

Mole ratios, derived from balanced equations, are fundamental to stoichiometry calculations. These ratios are used to convert moles of one substance into moles of another substance involved in the reaction.

Balanced Chemical Equations

Balanced chemical equations are representations of chemical reactions that respect the conservation of mass. In a balanced equation, the number of atoms of each element in the reactants side is equal to that in the products side. This balance is mandatory to accurately perform stoichiometry calculations.

The balancing of a chemical equation involves the adjustment of coefficients—these are the numbers placed before the compounds—in order to make the number of atoms of each element consistent on both sides of the equation. Each coefficient multiplies all the atoms in the compound that follows it.

Visualizing The Reaction

For learners, visual aids such as atomic drawings or molecular models can be helpful in understanding how atoms and molecules interact and recombine during reactions.

Stoichiometry Calculation

Stoichiometry calculations are mathematical processes used to determine the amounts of substances consumed and produced in a chemical reaction. Calculations often start with a balanced chemical equation, which provides the mole ratios necessary to convert between substances.

The steps include identifying the limiting reactant, which is the reactant that will be used up first and thus, dictates the amount of product that can be formed. The mole ratio from the balanced equation is then used to convert moles of the limiting reactant into moles of the desired product.

Executing Stoichiometry Problems

In practice, to solve stoichiometry problems like the exercise provided, students must first balance the equation, identify the limiting reactant, and then use it with the appropriate mole ratios to find the quantity of product produced. Comprehension of each step and its importance can greatly enhance problem-solving skills in stoichiometry.