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Chapter 1: Problem 65

A solution of sucrose in water is \(28.0 \%\) sucrose by mass and has a density of \(1.118 \mathrm{g} / \mathrm{mL} .\) What mass of sucrose, in grams, is contained in 3.50 L of this solution?

Short Answer

Expert verified
The mass of sucrose in 3.50 L of this solution is approximately 1096 g.

Step by step solution

01

Convert volume to mass

The problem involves using the solution's density to convert the given volume to mass. This is done by multiplying the volume of the solution by its density: \(mass = volume \times density\). Here, the volume is 3.50 L (or 3500 mL, because 1 L = 1000 mL), and the density is 1.118 g/mL. So, the mass of the solution is \(3500 \, \mathrm{mL} \times 1.118 \, \mathrm{g/mL} = 3913 \, \mathrm{g}\).
02

Calculate the mass of sucrose

Next, use the provided concentration of sucrose (28.0% by mass) to find the mass of sucrose in this solution. Keep in mind that the phrase '28.0% by mass' means that 28.0 g of sucrose are in every 100 g of solution. So, to find the mass of sucrose in 3913 g of solution, simply multiply the total mass of the solution by the concentration of sucrose: \(mass \, of \, sucrose = mass \, of \, solution \times concentration = 3913 \, \mathrm{g} \times 0.280 = 1095.64 \, \mathrm{g}\). Therefore, the mass of sucrose in 3.50 L of this solution is roughly 1096 g, assuming that the percentage is accurate to three significant figures.

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Most popular questions from this chapter

A solution consisting of \(8.50 \%\) acetone and \(91.5 \%\) water by mass has a density of \(0.9867 \mathrm{g} / \mathrm{mL} .\) What mass of acetone, in kilograms, is present in 7.50 L of the solution?

The highest temperature of the following group is (a) \(217 \mathrm{K} ;\) (b) \(273 \mathrm{K} ;\) (c) \(217^{\circ} \mathrm{F} ;\) (d) \(105^{\circ} \mathrm{C} ;\) (e) \(373 \mathrm{K}\).

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