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Chapter 4: Problem 103

An average human being has about 5.0 \(\mathrm{L}\) of blood in his or her body. If an average person were to eat 32.0 \(\mathrm{g}\) of sugar (sucrose, $\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}, 342.30 \mathrm{g} / \mathrm{mol}$ ), and all that sugar were dissolved into the bloodstream, how would the molarity of the blood sugar change?

Short Answer

Expert verified
The molarity of the blood sugar would change by 0.0187 mol/L after the person eats 32.0 g of sugar.

Step by step solution

01

Convert grams of sugar to moles

To convert grams of sugar to moles, we need to use the molar mass given in the exercise \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}, 342.30 \mathrm{g} / \mathrm{mol}\). We have 32.0 g of sugar, so we can use the conversion factor: Moles of sugar = \(\frac{32.0 \,\mathrm{g}}{342.30\, \mathrm{g/mol}}\)
02

Calculate the volume of blood in liters

Given that an average human being has 5.0 L of blood, we can use this value as the volume in our molarity calculation. Volume of blood = 5.0 L
03

Calculate the molarity using moles and volume

To find the molarity, we will divide the moles of sugar by the volume of blood in liters. Molarity = \(\frac{\text{moles of sugar}}{\text{Volume of blood in L}}\) Plugging in the values: Molarity = \(\frac{\frac{32.0 \,\mathrm{g}}{342.30\, \mathrm{g/mol}}}{5.0\,\mathrm{L}} = 0.0187\, \mathrm{mol/L}\) Hence, the molarity of the blood sugar would change by 0.0187 mol/L after the person eats 32.0 g of sugar.

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