The osmotic pressure of blood is 7.65 atm at 37 °C.What mass of glucose (C₆H₁₂O₆,molar mass = 180.2 g/mol)is needed to prepare 2.25 L of solution for intravenous injection? The osmotic pressure of the glucose solution must equal the osmotic pressure of blood.(R = 0.08206 L⋅atm/mol⋅K) A) 0.676 g B) 0.698 g C) 5.67 g D) 122 g E) 1.02 × 10³ g

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Quizplus · Accepted Answer

To find the mass of glucose needed, we use the formula for osmotic pressure: $\pi = MRT$, where $\pi$ is the osmotic pressure, $M$ is the molarity, $R$ is the gas constant, and $T$ is the temperature in Kelvin. Given $\pi = 7.65$ atm, $R = 0.08206$ L⋅atm/mol⋅K, and $T = 37$ °C (which is $310$ K when converted), we can solve for $M$, the molarity of the glucose solution. First, rearrange the formula to solve for $M$: $M = \frac{\pi}{RT}$.Substitute the given values: $M = \frac{7.65}{0.08206 \times 310}$.Solving for $M$ gives approximately $0.3$ mol/L.To find the mass of glucose needed for $2.25$ L of solution, multiply the molarity by the volume of the solution and the molar mass of glucose: mass = $M \times \text{volume} \times \text{molar mass}$ = $0.3 \times 2.25 \times 180.2$.This calculation gives a mass of approximately $122$ g.

The Osmotic Pressure of Blood Is 7