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A chemistry student must write down in her lab notebook the concentration of a solution of sodium hydroxide. The concentration of a solution equals the mass of what's dissolved divided by the total volume of the solution. Here's how the student prepared the solution: The label on the graduated cylinder says: empty weight: She put some solid sodium hydroxide into the graduated cylinder and weighed it. With the sodium hydroxide added, the cylinder weighed . She added water to the graduated cylinder and dissolved the sodium hydroxide completely. Then she read the total volume of the solution from the markings on the graduated cylinder. The total volume of the solution was . What concentration should the student write down in her lab notebook? Be sure your answer has the correct number of significant digits.

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Answer:

  • M = 2.294 mol / liter (four significant figures)

Explanation:

The molar concentration is calculated as the ratio of solute moles to liters of solution:

  • M = number of moles of solute / volume of solution in liters.

The volume of the solution is the given in mililiters, 127.53 ml, so you have to convert it to liters:

  • 127.53 ml × 1 liter / 1,000 ml = 0.12753 liter

The moles of solute is calcuated using the molar mass and the formula:

  • moles = mass in grams / molar mass

The molar mass of sodium hydroxide (NaOH) is 39.997 g/mol

The mass in grams of the sodium hydroxide solution is calculated by difference:

  • mass of sodium hydroxide = mass of the cylinder with the sodium hydroxide added - mass of empty cylinder

  • mass of sodium hydroxide = 13.195 g - 1.50 g = 11.695 g

Using the rule for signficant figures, when subtracting measures, that mass must be rounded to two decimal places, which is the least number of decimals of the amounts being subtracted, so the mass of sodium hydroxide is 11.70 g.

  • mass of sodium hydroxide = 11.70g (4 signficant digits)

Then,

  • n = 11.70 g / 39.997 g/mol ≈ 0.2925 mol

Compute the molarity:

  • M = [ 11.70 g / 39.997 mol ] / 0.12753 liter

            = 2.294mol / liter ← answer

Note: I divided directly [ 11.70 / 33.997] by 0.12753, instead of 0.2925 by 0.12753, to avoid intermediate roundings that may change the last signficant digit.

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