Question

We add excess NaCl solution (58.44 g/mol) to 72 mL of a solution of silver nitrate (AgNO3 169.88 g/mol), to form insoluble solid AgCl. When it has been dried and weighed, the mass of AgCl (143.32 g/mol) is found to be 2.61 grams. What is the molarity of the original AgNO3 solution? The formula weight of NaNO3 is 85.00 g/mol.

Answer 1

Answer:

The molarity of the original AgNO3 solution is 0.2529 M

Explanation:

Step 1:  The balanced equation

AgNO3 + NaCL → AgCl + NaNO3

This means that for 1 mole of AgNO3 consumed, 1 mole of NaCL will be consumed, to produce 1 mole of AgCL and 1 mole of NaNO3

Step 2: Calculating moles of AgCl

Moles of AgCl = mass of AgCL / Molar mass of AgCL

moles of AgCl = 2.61 grams / 143.32g/mole

moles of AgCl = 0.01821 moles

Step 3: Calculating moles of AgNO3

Since there is consumed 1 mole of AgNO3 to produce 1 mole of AgCl, this means that if there is produced 0.01821 moles of AgCl, there is consumed also 0.01821 moles of AgNO3

Step 4: Calculating molarity of AgNO3

Molarity of AgNO3 = moles of AgNO3 / volume of AgNO3

Molarity of AgNO3 = 0.01821 moles/  0.072 L = 0.2529 M = 0.2529 mol/L

The molarity of the original AgNO3 solution is 0.2529 M

Answer 2

Taking into account definition of molarity, the molarity of the original AgNO₃ solution is 0.2529 $\frac{moles}{liters}$.

Reaction stoichiometry

In first place, the balanced reaction is:

AgNO₃ + NaCL → AgCl + NaNO₃

By reaction stoichiometry (that is, the relationship between the amount of reagents and products in a chemical reaction), the following amounts of moles of each compound participate in the reaction:

• AgNO₃: 1 mole
• NaCl: 1 mole
• AgCl: 1 mole
• NaNO₃: 1 mole

Definition of molarity

Molar concentration or molarity is a measure of the concentration of a solute in a solution and indicates the number of moles of solute that are dissolved in a given volume.

The molarity of a solution is calculated by dividing the moles of solute by the volume of the solution:

$molarity=\frac{number of moles}{volume}$

Molarity is expressed in units $\frac{moles}{liters}$.

Moles of AgCl formed

When it has been dried and weighed, the mass of AgCl is found to be 2.61 grams. Being the molar mass 143.32 g/mole, the moles of AgCl formed is calculated as:
$2.61 gramsx\frac{1 mole}{143.32 grams} =$ 0.01821 moles

Moles of AgNO₃ needed

The following rule of three can be applied: if by reaction stoichiometry 1 mole of AgCl is formed by 1 mole of AgNO₃, 0.01821 moles of AgCl is formed by how many moles of AgNO₃?

$moles of AgNO_{3} =\frac{0.01821 moles of AgClx1 mole of AgNO_{3}}{1 mole of AgCl}$

moles of AgNO₃= 0.01821 moles

Then, 0.01821 moles of AgCl can be produced from 0.01821 moles of AgNO₃.

Molarity of AgNO₃

You know:

• number of moles= 0.01821 moles
• volume= 72 mL= 0.072 L

Replacing on the definition of molarity:

$molarity=\frac{0.01821 moles}{0.072 L}$

Solving:

molarity= 0.2529 $\frac{moles}{liters}$

Finally, the molarity of the original AgNO₃ solution is 0.2529 $\frac{moles}{liters}$.

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