Question

Calculate the sodium ion concentration when 70.0 mL of 3.0 M sodium carbonate is added to 30.0 mL of 1.0 M sodium bicarbonate.

Short answer

The concentration of sodium ions in the final solution after mixing 70.0 mL of 3.0 M sodium carbonate and 30.0 mL of 1.0 M sodium bicarbonate is 4.5 M.

Step-by-step solution

Identify the chemical formulas of the compounds

The chemical formula for sodium carbonate is Na2CO3 and for sodium bicarbonate, it is NaHCO3. Notice that sodium carbonate has two sodium atoms per molecule, which can form separate Sodium ions, while sodium bicarbonate has one sodium atom per molecule.

Calculate the moles of sodium ions in each solution separately

To calculate the moles of sodium ions in each solution, use the formula: Moles = Volume (L) × Concentration (M) For sodium carbonate: Moles_Na2CO3 = 70.0 mL × (3.0 mol/L) × (1 L / 1000 mL) = 0.21 mol Since there are two sodium ions per molecule, the moles of sodium ions will be: Moles_Na+ = 2 × Moles_Na2CO3 =2 × 0.21 mol = 0.42 mol For sodium bicarbonate: Moles_NaHCO3 = 30.0 mL × (1.0 mol/L) × (1 L / 1000 mL) = 0.03 mol Since there is only one sodium ion per molecule, the moles of sodium ions will be the same as the moles of sodium bicarbonate: Moles_Na+ = Moles_NaHCO3 = 0.03 mol

Add the moles of sodium ions together

Now that we have the moles of sodium ions from each solution, we add them together to get the total moles of sodium ions: Total moles_Na+ = Moles_Na+ (from Na2CO3) + Moles_Na+ (from NaHCO3) = 0.42 mol + 0.03 mol = 0.45 mol

Calculate the final volume of the mixed solution

To calculate the final volume, simply add the volume of each solution: Final volume = Volume_Na2CO3 + Volume_NaHCO3 = 70.0 mL + 30.0 mL = 100 mL Convert the final volume to liters: Final volume = 100 mL × (1 L / 1000 mL) = 0.1 L

Calculate the concentration of sodium ions in the final solution

To find the concentration, divide the total moles of sodium ions by the final volume: Concentration_Na+ = Total moles_Na+ / Final volume = 0.45 mol / 0.1 L = 4.5 M So, the concentration of sodium ions in the final solution is 4.5 M.

Key concepts

Chemical Formulas

When we talk about chemical formulas, we are essentially identifying the composition of molecules. For sodium carbonate, the formula is \( ext{Na}_2 ext{CO}_3 \). This means each molecule contains two sodium (Na) atoms, one carbon (C) atom, and three oxygen (O) atoms. On the other hand, sodium bicarbonate has the formula \( ext{NaHCO}_3 \). Here, one sodium atom is combined with one hydrogen (H) atom, one carbon atom, and three oxygen atoms.

• Each sodium carbonate molecule can release two sodium ions because it has two sodium atoms.
• Each sodium bicarbonate molecule releases one sodium ion as it contains one sodium atom.

Understanding these formulas is crucial, as it helps determine how many sodium ions are produced when these compounds dissolve in water.

Moles Calculation

Moles are a fundamental concept in chemistry used to denote a specific amount of a substance. To find the moles of a substance, you use the formula: \( ext{Moles} = ext{Volume (L)} \times ext{Concentration (M)} \). For instance, when we have 70.0 mL of 3.0 M sodium carbonate, we calculate the moles of sodium carbonate as:\[ ext{Moles}_{ ext{Na}_2 ext{CO}_3} = 70.0 ext{ mL} \times 3.0 ext{ mol/L} \times (1 ext{ L} / 1000 ext{ mL}) = 0.21 ext{ mol}\]Similarly, for 30.0 mL of 1.0 M sodium bicarbonate:\[ ext{Moles}_{ ext{NaHCO}_3} = 30.0 ext{ mL} \times 1.0 ext{ mol/L} \times (1 ext{ L} / 1000 ext{ mL}) = 0.03 ext{ mol}\]This calculations help in determining the amount of sodium available in each solution.

Solution Mixing

When you mix solutions, you combine volumes and their substances together. In this exercise, mixing 70.0 mL of one solution with 30.0 mL of another leads to a total volume of 100 mL. The mixed solution now contains the combined moles of sodium ions from both sodium carbonate and sodium bicarbonate:

• From sodium carbonate: 0.42 mol of sodium ions.
• From sodium bicarbonate: 0.03 mol of sodium ions.

Adding these gives a total amount of 0.45 mol of sodium ions. It's important to note that the moles of ions simply add up in the new joint solution, while the volumes contribute to the new total volume.

Molarity Calculation

Molarity is a measure of how concentrated a solution is. It is calculated by dividing the total moles of solute by the total volume of solution in liters: \( ext{Molarity} = ext{Total moles} / ext{Total volume} \). After mixing the two solutions, we have:- Total moles of sodium ions: 0.45 mol- Total volume of solution: 100 mL, which is 0.1 L in liters.The molarity of the combined solution is:\[ ext{Concentration}_{ ext{Na}^+} = rac{0.45 ext{ mol}}{0.1 ext{ L}} = 4.5 ext{ M}\]This tells us that the final sodium ion concentration in the mixed solution is 4.5 molar, or 4.5 M. Understanding molarity is essential in chemistry as it gives a clear idea of the solute concentration in a solution, which can affect reactions and processes.