Question

\begin{aligned} &\text { Which is more concentrated with respect to sodium ions, } 0.50 \mathrm{M} \mathrm{NaCl} \text { or } 0.30 \mathrm{M}\\\ &\mathrm{Na}_{2} \mathrm{SO}_{4} ? \end{aligned}

Short answer

The 0.30 M Na2SO4 solution is more concentrated with respect to sodium ions.

Step-by-step solution

Prepare the stoichiometry of the chemical reaction

For every molecule of NaCl that dissolves in solution, it produces one sodium ion (Na+). Therefore, the concentration of sodium ions in a 0.50 M NaCl solution is also 0.50 M. For every molecule of Na2SO4 that dissolves, it yields two sodium ions, because the formula (Na2) indicates there are two sodium ions for each sulfate ion in the compound. Therefore, the sodium ion concentration is twice the original concentration of Na2SO4.

Calculate sodium ion concentration for NaCl

The concentration \([Na^+]\) of the sodium ion in 0.50M NaCl is equal to 0.50M since the number of moles of sodium ions produced by one mole of NaCl is 1. Therefore, the sodium ion concentration in a 0.50M NaCl solution is 0.50M.

Calculate sodium ion concentration for Na2SO4

Now, to calculate the concentration \([Na^+]\) of sodium ions for the 0.30 M Na2SO4 solution, we multiply the moles of Na2SO4 by 2 because each molecule of Na2SO4 produces two sodium ions, so \(0.30 \, M * 2 = 0.60 \, M\). Therefore, the sodium ions concentration in a 0.30 M Na2SO4 solution is 0.60 M.

Key concepts

Stoichiometry

Understanding stoichiometry is crucial for solving problems involving chemical reactions and concentrations. It involves the quantitative relationships between the amounts of reactants and products in a chemical reaction. When it comes to dissolution of salts in water, stoichiometry allows us to calculate the concentration of ions in solution after the salt has dissociated.

For instance, the dissolution of sodium chloride (NaCl) produces an equal number of sodium (Na⁺) and chloride (Cl⁻) ions. If we begin with a 0.50 M NaCl solution, stoichiometry dictates that the concentration of sodium ions will also be 0.50 M, since there is a one-to-one ratio of NaCl to Na⁺ ions.

Real-world Applications

Useful in laboratory work and industry, stoichiometry is used to predict the yield of products obtained in a chemical reaction, ensuring that processes are both efficient and cost-effective. It is also applied in environmental science to assess pollutant dispersal and in medicine to calculate drug doses.

Molarity

Molarity, often represented by the symbol M, is the measure of the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution, giving the units moles per liter (mol/L). It's important for students to comprehend how molarity relates to the stoichiometry of dissolved substances.

When dissolving salts, such as NaCl and Na₂SO₄, their molarity can be used to determine the concentration of individual ions. For example, a 0.50 M solution of NaCl produces a sodium ion concentration of 0.50 M, as each unit of NaCl gives one Na⁺ ion. However, the relationship is not always one-to-one.

Adjusting for Compound Stoichiometry

The molarity of ions originating from polyatomic ionic compounds requires consideration of the stoichiometry. In the case of Na₂SO₄, for each formula unit that dissolves, two Na⁺ ions are released. So, a 0.30 M Na₂SO₄ solution yields a 0.60 M concentration of sodium ions.

Dissolution of Salts

The dissolution of salts into ions in a solvent, typically water, is a foundational chemical concept. Not all salts dissolve to the same extent; some are highly soluble, while others are not. When a soluble salt like NaCl or Na₂SO₄ dissolves in water, it dissociates into its constituent anions and cations.

The degree of dissolution and the stoichiometry of the salt dictate the resulting concentration of ions. Taking Na₂SO₄ as an example, we understand that for every unit of Na₂SO₄ that dissolves, two Na⁺ ions are formed. This stoichiometric relationship is vital for correctly determining the concentration of each type of ion in solution.

Impact on Physical Properties

The concentration of ions has notable effects on the physical properties of solutions, such as boiling point elevation and freezing point depression. It also influences the conductivity and reactivity of the solution, which are important aspects in fields such as biochemistry and engineering.