A Concentrated Phosphoric Acid Solution Is 85.5% H₃PO₄

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A concentrated phosphoric acid solution is 85.5% H₃PO₄ by mass and has a density of 1.69 g/mL at 25°C. What is the molarity of H₃PO₄? What is the mole fraction of urea, CO(NH₂)₂, in a solution prepared by dissolving 5.6 g of urea in 30.1 g of methanol, CH₃OH? How will an understanding of this concept help you in your healthcare career?

Paper For Above instruction

Understanding the molarity of phosphoric acid and the mole fraction of urea in solutions provides fundamental insights into solution chemistry, which are vital in various healthcare applications, such as medication formulation, diagnostics, and treatment strategies. This paper explores the calculation of molarity from a concentrated phosphoric acid solution, determines the mole fraction of urea in methanol, and discusses the relevance of these concepts in the healthcare field.

Calculating the Molarity of Phosphoric Acid

The problem states that the phosphoric acid (H₃PO₄) solution is 85.5% by mass with a density of 1.69 g/mL at 25°C. First, we determine the number of grams of H₃PO₄ in 1 liter (1000 mL) of solution:

• Mass of solution per liter = 1.69 g/mL × 1000 mL = 1690 g
• Mass of H₃PO₄ in this solution = 85.5% of 1690 g = 0.855 × 1690 g ≈ 1443.95 g

Next, calculate the molar mass of H₃PO₄:

• Atomic masses: H = 1.008 g/mol, P = 30.974 g/mol, O = 16.00 g/mol
• Molar mass of H₃PO₄ = (3 × 1.008) + 30.974 + (4 × 16.00) ≈ 97.994 g/mol

Number of moles of H₃PO₄ in 1 liter:

1443.95 g / 97.994 g/mol ≈ 14.75 mol

Thus, the molarity of the phosphoric acid solution is approximately 14.75 M.

Calculating the Mole Fraction of Urea

For urea dissolved in methanol, we are given:

- Mass of urea = 5.6 g

- Mass of methanol = 30.1 g

Moles of urea:

• Molar mass of urea (CO(NH₂)₂) = 12.01 (C) + 16.00 (O) + 2 × [14.01 (N) + 1.008 (H)] ≈ 60.06 g/mol
• Moles of urea = 5.6 g / 60.06 g/mol ≈ 0.0933 mol

Moles of methanol:

• Molar mass of CH₃OH = 12.01 (C) + 4 × 1.008 (H) + 16.00 (O) ≈ 32.04 g/mol
• Moles of methanol = 30.1 g / 32.04 g/mol ≈ 0.9385 mol

Mole fraction of urea:

X_urea = moles of urea / (moles of urea + moles of methanol) = 0.0933 / (0.0933 + 0.9385) ≈ 0.090

Implications in Healthcare

A thorough understanding of solution concentrations, molarity, and mole fractions is pivotal in healthcare practice. These concepts enable accurate drug formulation, ensuring proper dosing and bioavailability. For example, in intravenous solutions, precise molarity is essential to maintain safe osmolarity levels, preventing hemolysis or dehydration. Calculating mole fractions helps in understanding drug interactions and compatibility in multi-component pharmaceuticals. Moreover, knowledge of solution chemistry underpins diagnostic techniques such as spectrophotometry and chromatography, fundamental in disease detection and monitoring (Lyman et al., 2015). Therefore, mastering these concepts improves the safety, efficacy, and precision of patient care.

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