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Chapter 13: Problem 95

Glucose makes up about \(0.10 \%\) by mass of human blood. Calculate the concentration in (a) ppm, (b) molality. What further information would you need to determine the molarity of the solution?

Short Answer

Expert verified
The concentration of glucose in blood is 0.10% by mass. To find the concentration in ppm, we convert this percentage to parts per million: \(ppm = \frac{0.10}{100} \times 10^6 = 1000 \, ppm\). To find the molality, we first calculate the mass of glucose in 1 kg of blood: \(Mass \, of \, glucose = \frac{0.10}{100} \times 1000 = 1 \, g\). Then, find the moles of glucose (\(\frac{1g}{180.16g/mol} = 0.00555 \, mol\)). Molality is calculated as \(\frac{0.00555 \, mol}{1 \, kg \, solvent} = 0.00555 \, mol/kg\). To determine the molarity, the volume of the solution is needed.

Step by step solution

01

Write down the given mass percent concentration

The given mass percent concentration of glucose in human blood is 0.10%.
02

Convert the mass percent concentration to parts per million (ppm)

Since percent means per 100, we'll divide 0.10 by 100 to obtain a unitless ratio. Multiply it by 10^6 (1 million) to convert it to parts per million (ppm). Parts per million (ppm) = \(\frac{0.10}{100} \times 10^6\) ppm #a) Calculating molality#
03

Calculate the mass of glucose in 1 kg of blood

We know that glucose is 0.10% by mass of human blood. So, in 1 kg of blood (1000 g), the mass of glucose will be: Mass of glucose = \(\frac{0.10}{100} \times 1000\) g
04

Calculate the moles of glucose

To calculate the molality, we need to know the moles of solute (glucose in this case). The molar mass of glucose (C6H12O6) is 180.16 g/mol. So, the moles of glucose in 1 kg of blood are: Moles of glucose = \(\frac{\text{Mass of glucose}}{\text{Molar mass of glucose}}\)
05

Calculate molality

Now we have the moles of glucose and the mass of the solvent (human blood without glucose) in kilograms. Use the following formula to calculate the molality: Molality = \(\frac{\text{Moles of solute}}{\text{Mass of solvent in kg}}\)
06

Answering the question regarding molarity

Molarity is the number of moles of solute per liter of solution. To determine the molarity of this solution, we need to know the volume of the solution and the moles of glucose present in that volume. In summary: 1. Calculate the ppm concentration by converting the given mass percent concentration. 2. Calculate the molality using the mass and moles of glucose and the mass of solvent. 3. To determine the molarity, the volume of the solution is needed.

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