Question

Calculate the sodium ion concentration when \(70.0 \mathrm{~mL}\) of \(3.0 \mathrm{M}\) sodium carbonate is added to \(30.0 \mathrm{~mL}\) of \(1.0 \mathrm{M}\) sodium bicarbonate.

Short answer

The sodium ion concentration in the mixture is \(4.5 M\).

Step-by-step solution

Put the sodium ion concentration into perspective

To reach our goal, we will focus on the number of moles of sodium ions which are provided by each solution, and then divide this sum by the total volume of the mixture. Moreover, we have to remember that sodium carbonate (Na2CO3) provides 2 moles of Na⁺ ions per mole of Na2CO3 and sodium bicarbonate (NaHCO3) provides 1 mole of Na⁺ ions per mole of NaHCO3.

Calculate the number of moles of Na2CO3 and NaHCO3 in the solutions

Since we have the molarity (M) and the volume (V) of each solution, we can calculate the number of moles (n) using the formula: n = M * V For sodium carbonate: M = 3.0 M V = 70.0 mL = 0.070 L n(Na2CO3) = 3.0 * 0.070 = 0.21 moles For sodium bicarbonate: M = 1.0 M V = 30.0 mL = 0.030 L n(NaHCO3) = 1.0 * 0.030 = 0.03 moles

Determine the number of moles of sodium ions contributed by each substance

As mentioned before, we know that each mole of Na2CO3 will provide 2 moles of Na⁺ ions and each mole of NaHCO3 will give us 1 mole of Na⁺ ions. n(Na⁺ from Na2CO3) = 2 * n(Na2CO3) = 2 * 0.21 = 0.42 mol n(Na⁺ from NaHCO3) = 1 * n(NaHCO3) = 1 * 0.03 = 0.03 mol Now, let's find the total moles of Na⁺ ions: n(Na⁺ total) = n(Na⁺ from Na2CO3) + n(Na⁺ from NaHCO3) = 0.42 + 0.03 = 0.45 mol

Find the final volume of the mixture

To find the final volume, we just need to add the volumes of the two initial solutions: V(total) = V(Na2CO3) + V(NaHCO3) = 0.070 + 0.030 = 0.100 L

Calculate the concentration of sodium ions in the mixture

Finally, to find the sodium ion concentration, we can use the formula: M(Na⁺) = n(Na⁺ total) / V(total) M(Na⁺) = 0.45 mol / 0.100 L = 4.5 M The sodium ion concentration in the mixture is 4.5 M.

Key concepts

Molarity

Molarity is a measurement of concentration used in chemistry to express the amount of a substance in a given volume of solution. It's denoted by the symbol 'M' and is defined as the number of moles of solute per liter of solution.

For example, if you have a solution where 1 mole of a substance is dissolved in 1 liter of solution, then the molarity of that solution is 1 M. When calculating concentrations, it's crucial to convert volumes to liters, as molarity is concerned with liters of solution. In practical terms, molarity allows you to understand how much of a particular substance is present in a solution and enables you to predict how that solution will react in different chemical scenarios.

Stoichiometry

Stoichiometry is the part of chemistry that deals with the relative quantities of reactants and products in chemical reactions. It is founded on the law of conservation of mass where the total mass of the reactants equals the total mass of the products.

Understanding stoichiometry is vital when trying to calculate the quantities involved in a chemical reaction, as this knowledge enables you to manipulate and measure those quantities. For example, if a molecule of sodium carbonate decomposes into ions in water, stoichiometry allows for calculating the exact amount of sodium ions produced.

Sodium Carbonate

Sodium carbonate, often known as soda ash or washing soda with the formula Na2CO3, is a sodium salt of carbonic acid. It's a commonly used chemical in laboratories and various industries including glass manufacturing, paper production, and detergents.

When dissolved in water, sodium carbonate dissociates into sodium ions (Na⁺) and carbonate ions (CO3²⁻). Each molecule of sodium carbonate yields two moles of sodium ions, as indicated by the chemical formula. In the context of stoichiometry, this information is essential for calculating the contribution of sodium carbonate to the sodium ion concentration in solution.

Sodium Bicarbonate

Sodium bicarbonate, known as baking soda with the chemical formula NaHCO3, is another sodium salt of carbonic acid. It's widely used in baking, as a leavening agent, and for neutralizing acids.

In aqueous solutions, sodium bicarbonate dissociates into one mole of sodium ions and one mole of bicarbonate ions. For every mole of sodium bicarbonate, one mole of sodium ions is released into the solution, which is fundamental for accurately calculating the total sodium ion concentration when sodium bicarbonate is mixed with other sodium-containing compounds such as sodium carbonate.