The pharmacy receives a new order to prepare a hypertonic 3% saline drip for a newly admitted patient. How many millimoles of sodium do two and three-fourths liters of thisinfusion solution deliver? Round to the nearest increment of 250. (AW: sodium = 23,chloride = 35.5)
The correct answer and explanation is:
Let’s break down the problem step-by-step to find how many millimoles (mmol) of sodium are in 2.75 liters of 3% saline solution.
Step 1: Understand the concentration of 3% saline
- A 3% saline solution means 3 grams of NaCl per 100 mL of solution.
- Since 3% = 3 g/100 mL, in 1 liter (1000 mL), the amount of NaCl is: 3 g100 mL×1000 mL=30 g NaCl per liter\frac{3\, \text{g}}{100\, \text{mL}} \times 1000\, \text{mL} = 30\, \text{g NaCl per liter}
Step 2: Calculate the total amount of NaCl in 2.75 liters
30 g/L×2.75 L=82.5 g NaCl30\, \text{g/L} \times 2.75\, \text{L} = 82.5\, \text{g NaCl}
Step 3: Calculate the amount of sodium (Na⁺) in grams
- Sodium chloride (NaCl) consists of sodium (Na) and chloride (Cl).
- Molar masses: Na = 23 g/mol, Cl = 35.5 g/mol
- Molar mass of NaCl = 23 + 35.5 = 58.5 g/mol
- Calculate moles of NaCl: moles NaCl=82.5 g58.5 g/mol≈1.41 mol\text{moles NaCl} = \frac{82.5\, \text{g}}{58.5\, \text{g/mol}} \approx 1.41\, \text{mol}
- Since each mole of NaCl contains 1 mole of Na⁺, moles of Na⁺ = 1.41 mol.
Step 4: Convert moles of sodium to millimoles
1.41 mol=1410 mmol1.41\, \text{mol} = 1410\, \text{mmol}
Step 5: Round to the nearest increment of 250
- 1410 mmol rounded to the nearest 250 = 1,250 mmol (since 1410 is closer to 1250 than to 1500)
Final answer:
The 2.75 liters of 3% saline solution deliver approximately 1,250 millimoles of sodium.
Explanation:
A 3% saline solution is a hypertonic solution containing 3 grams of sodium chloride per 100 milliliters. To find how much sodium it provides, we first convert the percentage concentration to grams per liter, giving 30 grams per liter. For 2.75 liters, this equals 82.5 grams of NaCl.
Next, using the molecular weight of sodium chloride (58.5 g/mol), we convert grams to moles. Each mole of NaCl contains exactly one mole of sodium ions, so the moles of NaCl equal the moles of sodium. Then, by converting moles to millimoles (1 mol = 1000 mmol), we find the total millimoles of sodium.
Rounding to the nearest 250 mmol increment is a typical practice in clinical calculations to match dosing and measurement convenience, resulting in approximately 1250 mmol of sodium in the entire infusion.
This calculation is important in clinical settings, as the sodium load delivered through IV fluids affects the patient’s electrolyte balance, fluid status, and overall treatment plan. Hypertonic saline must be dosed carefully to avoid complications like hypernatremia or fluid shifts.