Question

Calculate the molarity of an aqueous solution that is 18.2% by mass calcium chloride. You might need to know that the density is 1.18 g/ml.

Answer 1

The Molarity of the aqueous solution that is 18.2% by mass calcium chloride is 1.94 moles/liter.

Key points:

• Molarity is the concentration of a solution in moles per liter. It is calculated by dividing the number of moles of a solution, n by its volume in liters, V. That is; Molarity = n/V
• When given the molarity of a solution and the volume of the solution then we can get the number of moles, by multiplying the molarity by volume; n = MV.
• Number of moles of a compound can also be given by dividing the mass of the compound by its relative molecular mass.
• The percentage by mass is given by;

= (mass of solute/mass of the solution)×100%.

• Density of a solution is give by dividing the mass of a solution by its volume. That is; density = mass/volume.

Step by Step Explanation:

Step 1: Calculate the mass of the solute.

Percentage of solute by mass is 18.2%.

Assuming the mass of the solution to be 100g, then;

percentage by mass = (mass of solute/mass of the solution)×100%.

= 18.2 % = (x/100) × 100

= 0.182 = x/100

x = 18.2 g

Thus, mass of solute = 18.2 g

Step 2: Calculating the volume of the solution.

Density of the solution is 1.18 g/ml

But, density = mass/volume

Thus, Volume = mass/density

Mass of the solution is 100 g

Therefore;

Volume = 100 g/ 1.18 g/ml

= 84.75 mL or 0.08475 L

Step 3: Calculating the number of moles of the solute, Calcium chloride,

Number of moles = mass of solute/ molecular mass of solute

Mass of solute = 18.2 g

Molecular mass of Calcium chloride is 110.98 g/mol

Thus;

Number of moles = 18.2 g/110.98 g/mol

= 0.164 mole

Step 4: Calculating the molarity of the solution;

Molarity = number of moles/ volume in L

number of moles = 0.164 mole

Volume in L = 0.08475 L

Therefore;

Molarity = 0.164 mole/0.08475 L

= 1.94 moles/L or 1.94 M

Answer 2

• M = 1.94 mol/liter = 1.94 M

Step-by-step explanation:

1) Data:

a) M = ?

b) % mass = 18.2%

c) Solute: CaCl₂

d) d = 1.18 g/ml

2) Formulae:

a) Molarity

M = n/V, where M is molarity, n is number of moles of solute, and V is the volumen of solution in liters.

b) Density

d = m/V, where d is the density of the solution, m is the mass in grams, V is the volume in liters.

c) Number of moles

n = mass in grams / molar mass, where n is the number of moles.

d) % mass

% = (mass of solute / mass of solution) × 100

3) Solution:

a) Start by assuming a base amount: 100 g of solution.

b) Calcualte the volume (V) of the solution:

• d = m / V ⇒ V = m / d

V = 100 g / 1.18 g/ml = 84.75 ml

V = 0.08475 liter

c) Calculate the mass of solute:

• % = (mass of solute / mass of solution) × 100

⇒ mass of solute = % × mass of solution / 100 = 18.2 × 100 g / 100

mass of soiute = 18.2 g

d) Calculate the number of moles of solute (n)

• molar mass of CaCl₂ = 110.98 g/mol g/mol

• n =mass in grams / molar mass = 18.2 g / 110.98 g/mol = 0.164 mol

e) Calculate the molarity (M) of the solution

• M = n / V = 0.164 mol / 0.08475 liter = 1.94 mol/liter = 1.94 M

The answer is reported with 3 significant figures, since the data have 3 significant figures.