Question

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

Short answer

To bring the sodium ion concentration up to 0.138 M, approximately \(5.38\) grams of sodium chloride would need to be added to the blood, assuming no change in blood volume.

Step-by-step solution

Calculate the current moles of sodium ions

First, we need to find out how many moles of sodium ions are currently in the blood. The formula for converting concentration (M) to moles using volume (L) is: Moles = Concentration (M) × Volume (L) Using the given concentration and volume, we have: Moles = 0.118 M × 4.6 L Moles = \(0.5428\) moles So, there are currently \(0.5428\) moles of sodium ions in the blood.

Calculate the moles of sodium ions needed to reach the desired concentration

We now need to determine how many moles of sodium ions would be required to achieve the desired concentration of 0.138 M. Using the same formula as before: Moles_needed = Desired concentration (M) × Volume (L) Moles_needed = 0.138 M × 4.6 L Moles_needed = \(0.6348\) moles

Determine the moles of sodium ions to be added

By comparing the moles needed and the current moles of sodium ions, we can figure out how many moles of sodium ions will have to be added: Moles_to_add = Moles_needed - Current_moles Moles_to_add = \(0.6348 - 0.5428\) Moles_to_add = \(0.092\) moles Therefore, we need to add \(0.092\) moles of sodium ions to the blood.

Calculate the mass of sodium chloride to be added

We have found out that we need to add \(0.092\) moles of sodium ions to the blood. Since these ions come from sodium chloride (NaCl), we need to calculate the mass of NaCl required. First, we need to find the molar mass of NaCl. From the periodic table: Molar_mass_NaCl = Molar_mass_Na + Molar_mass_Cl Molar_mass_NaCl = \(22.99 g/mol + 35.45 g/mol\) Molar_mass_NaCl = \(58.44 g/mol\) Now, we can find out the mass of NaCl needed to provide the required moles of sodium ions: Mass_NaCl = Moles_to_add × Molar_mass_NaCl Mass_NaCl = \(0.092\) moles × \(58.44 g/mol\) Mass_NaCl = \(5.38 g\) So, we need to add approximately \(5.38\) grams of sodium chloride to the blood in order to reach the desired sodium ion concentration of 0.138 M, assuming no change in blood volume.