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Chapter 4: Problem 64

A person suffering from hyponatremia has a sodium ion concentration in the blood of \(0.118 M\) and a total blood volume of 4.6 L. What mass of sodium chloride would need to be added to the blood to bring the sodium ion concentration up to \(0.138 \mathrm{M}\), assuming no change in blood volume?

Short Answer

Expert verified
First, let's calculate the initial moles of sodium ions: Initial moles of sodium ions = 0.118 M × 4.6 L = 0.5428 moles Next, find the moles of sodium ions required for the target molarity: Moles of sodium ions required = 0.138 M × 4.6 L = 0.6348 moles Now, calculate the moles of sodium ions to be added: Moles of sodium ions to be added = 0.6348 moles - 0.5428 moles = 0.092 moles Finally, calculate the mass of sodium chloride to be added: Mass of NaCl = 0.092 moles × 58.44 g/mol = 5.38 g So, 5.38 grams of sodium chloride would need to be added to the blood to bring the sodium ion concentration up to 0.138 M, assuming no change in blood volume.

Step by step solution

01

Calculate the moles of sodium ions initially present

First, let's find the initial moles of sodium ions in the blood using the formula: Moles = Molarity × Volume Initial moles of sodium ions = 0.118 M × 4.6 L
02

Calculate the moles of sodium ions required for the target molarity

Next, let's find the moles of sodium ions required to achieve a molarity of 0.138 M using the same formula: Moles = Molarity × Volume Moles of sodium ions required = 0.138 M × 4.6 L
03

Calculate the moles of sodium ions to be added

Now we need to find the moles of sodium ions that need to be added to the blood by subtracting the initial moles of sodium ions from the required moles of sodium ions: Moles of sodium ions to be added = Moles of sodium ions required – Initial moles of sodium ions
04

Calculate the mass of sodium chloride to be added

Since each mole of sodium chloride (NaCl) produces one mole of sodium ions (Na+), the moles of NaCl to be added would be equal to the moles of sodium ions to be added. Now we can find the mass of NaCl required using the molar mass of NaCl (58.44 g/mol): Mass of NaCl = Moles of NaCl × Molar mass of NaCl Now let's plug in the values and do the calculations.

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