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 M, assuming no change in blood volume?

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Calculate the initial moles of sodium ions in the blood using the initial concentration (0.118 M) and the total blood volume (4.6 L). Use the formula: \( \text{moles} = \text{concentration} \times \text{volume} \).

Calculate the desired moles of sodium ions in the blood using the target concentration (0.138 M) and the total blood volume (4.6 L). Use the same formula: \( \text{moles} = \text{concentration} \times \text{volume} \).

Determine the additional moles of sodium ions needed by subtracting the initial moles from the desired moles.

Convert the additional moles of sodium ions to moles of sodium chloride (NaCl). Since each NaCl unit provides one Na\(^+\) ion, the moles of NaCl needed are equal to the additional moles of Na\(^+\).

Calculate the mass of sodium chloride required using the moles of NaCl and the molar mass of NaCl (58.44 g/mol). Use the formula: \( \text{mass} = \text{moles} \times \text{molar mass} \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molarity

Molarity (M) is a measure of concentration defined as the number of moles of solute per liter of solution. It is crucial for understanding how the concentration of sodium ions in the blood can be adjusted by adding sodium chloride. In this case, the initial and desired molarity of sodium ions will guide the calculation of the required mass of sodium chloride.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. In this scenario, it is used to determine the amount of sodium chloride needed to achieve the desired sodium ion concentration. Understanding the relationship between the moles of sodium ions and the moles of sodium chloride is essential for accurate calculations.

Mass Calculation

Mass calculation is the process of determining the mass of a substance based on its moles and molar mass. To find out how much sodium chloride to add, one must first calculate the moles of sodium ions needed to reach the target concentration and then convert that to mass using the molar mass of sodium chloride. This step is vital for practical applications in chemistry.