Question Video: Calculating the Molarity of a Solution from Mass and Volume | Nagwa Question Video: Calculating the Molarity of a Solution from Mass and Volume | Nagwa

# Question Video: Calculating the Molarity of a Solution from Mass and Volume Chemistry • First Year of Secondary School

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What is the molarity of a solution made by dissolving 21.5 g of sodium sulfate (NaβSOβ) in enough water to form 150 mL of solution? Give your answer to 3 decimal places. [O = 16 g/mol, Na = 23 g/mol, S = 32 g/mol]

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### Video Transcript

What is the molarity of a solution made by dissolving 21.5 grams of sodium sulfate, Na2SO4, in enough water to form 150 milliliters of solution? Give your answer to three decimal places. The molar mass of oxygen is 16 grams per mole, sodium is 23 grams per mole, and sulfur is 32 grams per mole.

Molarity, or molar concentration, is one of several ways to express the quantitative amount of solute in a solution. More specifically, molarity expresses the number of moles of solute per liter of solution. The molarity of a solution can be calculated using the equation π equals π divided by π£, where π is the molarity in moles per liter, π is the amount of solute in moles, and π£ is the volume of the solution in liters.

In the question, we are told that 21.5 grams of sodium sulfate are dissolved in water to form the solution. Since sodium sulfate is the substance being dissolved, it is the solute in this solution. We have been given the mass of the solute in grams, but we need to know the amount of solute in moles. We can use the equation π equals lowercase π divided by capital π to convert the mass in grams into an amount in moles. In this equation, π is the amount in moles, lowercase π is the mass in grams, and capital π is the molar mass in grams per mole. We know the mass, but we have not been given the molar mass of sodium sulfate. We have been given the average molar mass of oxygen, sodium, and sulfur. We can use these values to calculate the molar mass of sodium sulfate.

One formula unit of sodium sulfate contains two atoms of sodium, one atom of sulfur, and four atoms of oxygen. Each sodium atom has an average molar mass of 23 grams per mole. So two sodium atoms will have an average molar mass of 46 grams per mole. One sulfur atom has an average molar mass of 32 grams per mole. One oxygen atom has an average molar mass of 16 grams per mole, so four oxygen atoms will have an average molar mass of 64 grams per mole. Adding these molar masses together gives us the molar mass of sodium sulfate, 142 grams per mole.

Now, we can substitute the mass and molar mass into the equation. The grams unit will cancel, leaving us with a unit of moles. Performing the calculation gives us an amount of 0.1514 moles. We now know the value of π in the molarity equation. The question tells us that the volume of the solution is 150 milliliters. But in order to solve for molarity, the volume must be given in liters. We can convert between the two volume units by using the relationship one liter is equal to 1000 milliliters.

To perform the conversion, we can multiply the 150 milliliters given in the question by the relationship written as a fraction with the unit milliliters in the denominator so that the milliliter units cancel. Performing the calculation gives us a volume of 0.15 liters. Now that we have values for both π and π£, we can solve for the molarity. Dividing 0.1514 moles by 0.15 liters gives us a molarity of 1.00939 moles per liter. The question tells us to give our answer to three decimal places.

So, to three decimal places, the molarity of a solution made by dissolving 21.5 grams of sodium sulfate in enough water to form 150 milliliters of solution is 1.009 moles per liter.

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