How do I find the molarity and number of ions in this question

Question

A 54.0 mL solution had 5.90g of MgCl2 and 2.10 g of NaHCO3 dissolved with it. What is molarity of NaHCO3 in solution? What is molarity of chloride ions in solution? how many ions are there in solution?

Answer 1

Hello, Ivy,

To calculate the molarities, we need the molar masses of both compounds. Those are the sum of the atomic masses for each atom in each compound. For example, MgCl₂ has one Mg and 2 Cl atoms, for a total mass of 95.2 AMU, which can also be expressed as 95.2 g/mole. 95.2 grams of MgCl₂ is also Avogadro's number of molecules: 6.02x10²³.

Molarity is defined as moles/liter. We have the moles and volume of the sample, but the volume is in ml. Convert that to liters: 54.0 ml * (1 liter/1000ml) = 0.054 liters.

The moles of MgCl₂ is the mass of the sample divided by it's molar mass: 5.90g/(95.2 g/mole) = 0.061975 moles. We are limited to 3 sig figs, so the concentration is 0.0620M.

While we're on MgCl_2, let's calculate the number of ions from this compound. When dissolved, we get one Mg⁺² ion and 2 Cl^- ions. So there are 3 ions for every molecule. To get the number of molecules, multiply the number of moles of MgCl₂ times Avogadro's number. Then multiply that times the number of ions per molecule (3, in this case).

0.0620 moles * 6.02 x 10 ²³ molecules/mole * 3 ions/molecule= 1.12 x 10²³ ions

Look at how the units cancel to leave just ions.

The sodium bicarbonate is done exactly the same way. Add up the element AMU's to get the molar mass (g/mole) and divide the mass by the molar mass to get moles. Do the same steps as above to get the molarity. In this case, we also get three ions per molecule: The sodium(Na⁺), the hydrogen (H⁺), and the carbonate (CO₃^2-). Multiply the concentration (in M) times Avogadro's Number, time 3 to get the number of ions from the sodium bicarbonate.

Then add the ion count from both compounds to get the total ions.

I hope this helps,

Bob

Answer 2

First, to find molarity, we should look at the definition of molarity (M). It is the number of moles of solute per liter of solution. For this problem, we are given the volume of solution as 54.0 ml, so we convert that to liters, and we have 0.054 L. Now, we need to find moles of chloride ions.

Chloride ions come from the MgCl₂ only. And MgCl₂ dissociates into Mg²⁺ ions and 2Cl- ions. NOTE that there are TWO Cl- ions for each MgCl₂. Using dimensional analysis (unit factor method) we can find the moles of Cl- ions in 5.90 g of MgCl₂ as follows:

5.90 g MgCl₂ x 1 mol MgCl₂/95.2 g x 2 mol Cl-/mol MgCl₂ = 0.1239 moles Cl- ions

Molarity of Cl- ions = 0.1239 mol Cl-/0.054 L soln = 2.295 M = 2.30 M Cl- (3 sig. figs.)

I'll take the question of how many ions are there in solution to mean just that, and not the molarity of the various ions. That being the case, we will use Avogadro's number to convert moles of ions to number of ions. We already know Cl- = 0.1239 moles. We also know that Mg²⁺ = 1/2 of 0.1239 = 0.06195 moles Mg²⁺.

We now must include the NaHCO₃ which in water ==> Na⁺ + HCO₃^- ions.

molar mass NaHCO₃ = 84.0 g/mol

2.10 g NaHCO₃ x 1 mol NaHCO₃/84.0 g = 0.025 moles NaHCO₃ and since we get 2 moles of ions (Na⁺ and HCO₃^-) from each mole of NaHCO₃, we have 0.025 moles of Na⁺ and 0.025 moles of HCO₃^- ions.

Total moles of ions = 0.1239 mol Cl- + 0.06195 mol Mg²⁺ + 0.025 mol Na⁺ + 0.025 mol HCO₃^- = 0.2359 mols

NUMBER OF IONS = 0.2359 moles ions x 6.02x10²³ atoms/mol = 1.42x10²³ ions