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?

Short answer

Approximately $5.375\mathrm{g}$ of sodium chloride should be added to the blood to increase the sodium ion concentration to $0.138\mathrm{M}$ without any change in blood volume.

Step-by-step solution

Calculate the initial amount of sodium ions in the blood

To calculate the initial amount of sodium ions in the blood, we can use the formula: Initial amount of sodium ions = Initial concentration × Blood volume Let's plug in the given values: Initial concentration = 0.118 M Blood volume = 4.6 L Initial amount of sodium ions = $0.118\mathrm{M}\times 4.6\mathrm{L}$ = $0.5428\text{moles of sodium ions}$

Calculate the final amount of sodium ions required for the desired concentration

To calculate the final amount of sodium ions for a concentration of 0.138 M, we can use the same formula as in step 1: Final amount of sodium ions = Final concentration × Blood volume We have: Final concentration = 0.138 M Blood volume = 4.6 L Final amount of sodium ions = $0.138\mathrm{M}\times 4.6\mathrm{L}$ = $0.6348\text{moles of sodium ions}$

Calculate the net amount of sodium ions needed

Now, let's calculate the difference between the initial and final amount of sodium ions: Net amount of sodium ions needed = Final amount of sodium ions - Initial amount of sodium ions Net amount of sodium ions needed = $0.6348\text{moles}-0.5428\text{moles}$ = $0.092\text{moles of sodium ions}$

Calculate the mass of sodium chloride needed

Since sodium chloride (NaCl) dissociates into sodium ions (Na+) and chloride ions (Cl-) in a 1:1 ratio, the moles of sodium ions required will be equal to the moles of NaCl. To determine the mass of sodium chloride needed, we can use the formula: Mass of NaCl = Moles of NaCl × Molar mass of NaCl The molar mass of NaCl = 58.44 g/mol (22.99 g/mol for Na + 35.45 g/mol for Cl) Now let's calculate the mass of NaCl: Mass of NaCl = $0.092\mathrm{moles}\times 58.44\frac{\mathrm{g}}{\mathrm{mol}}$ = $5.375\mathrm{g}$ So, approximately 5.375 grams of sodium chloride should be added to the blood to increase the sodium ion concentration to 0.138 M without any change in blood volume.