Final answer:
To find the mass of glucose needed for the IV solution, use the osmotic pressure formula, rearrange to find molarity, then convert moles to grams using the molar mass of glucose, resulting in a) 91.6 g of glucose required.
Step-by-step explanation:
The mass of glucose required to make a 1.00 L aqueous solution with the same osmotic pressure as human blood at 37 °C is determined using the formula for osmotic pressure (Π) which is Π = MRT, where Π is the osmotic pressure, M is the molarity of the solution, R is the gas constant (0.0821 L atm mol−1 K−1), and T is the absolute temperature in Kelvin. In this case, the osmotic pressure of the solution (Π) must be equal to that of human blood, which is 7.6 atm.
First, rearrange the osmotic pressure formula to solve for the molarity (M): M = Π / (RT). Then, convert the temperature to Kelvin by adding 273.15 to the given temperature in Celsius. Finally, calculate the number of moles from the molarity and use the molar mass of glucose (180.16 g/mol) to find the mass.
Given the osmotic pressure of 7.6 atm and the temperature of 37 °C (which is 310.15 K), the calculation will yield the molarity, and multiplying the number of moles by the molar mass of glucose will give the required mass in grams. Using this approach, one can find that the answer is (a) 91.6 g.