Problem 64 - Chemistry: The Central Science

Question

A person suffering from hyponatremia has a sodium ion concentration in the blood of \(0.118 \mathrm{M}\) and a total blood volume of \(4.6 \mathrm{~L}\). 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?

Step-by-Step Solution

Answer

A mass of approximately \(5.376 \mathrm{g}\) 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.

Step 1: 1. Calculate the difference in sodium ion concentration

First, let's find the difference in sodium ion concentration: \[ Concentration\_difference = Target\_concentration - Current\_concentration \] In our case, the target concentration is \(0.138 \mathrm{M}\) and the current concentration is \(0.118 \mathrm{M}\). So, the difference in sodium ion concentration can be calculated as: \[ Concentration\_difference = 0.138 \mathrm{M} - 0.118 \mathrm{M} = 0.02 \mathrm{M} \]

Step 2: 2. Calculate the moles of sodium ions needed

Now that we know the concentration difference, let's find the number of moles of sodium ions needed to increase the concentration. To do this, we will use the formula: \[ Moles\_of\_sodium\_ions = Concentration\_difference \times Blood\_volume \] The blood volume is given as \(4.6 \mathrm{L}\), so the moles of sodium ions can be calculated as: \[ Moles\_of\_sodium\_ions = 0.02 \mathrm{M} \times 4.6 \mathrm{L} = 0.092 \mathrm{mol} \]

Step 3: 3. Convert moles of sodium ions to mass of sodium chloride

Finally, we'll convert the moles of sodium ions to the mass of sodium chloride (NaCl) needed to be added. The molar mass of NaCl is \(58.44 \mathrm{~g/mol}\) with the following relationship: \[ Mass\_of\_NaCl = Moles\_of\_sodium\_ions \times Molar\_mass\_of\_NaCl \] Now, we can calculate the mass of sodium chloride as: \[ Mass\_of\_NaCl = 0.092 \mathrm{mol} \times 58.44 \mathrm{~g/mol} = 5.376 \mathrm{g} \] So, a mass of approximately \(5.376 \mathrm{g}\) 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.