the osmotic pressure of blood at 37 degrees is 7.56atm. what mass of glucose should be dissolved per litre of solution for an intravenous injection to be isotonic with blood?
To determine the mass of glucose that should be dissolved per liter of solution for an intravenous injection to be isotonic with blood, we need to calculate the molarity of the glucose solution first. Then, we can use that information to determine the mass of glucose required.
Here's the step-by-step process to solve the problem:
Step 1: Determine the Osmotic Pressure of the Glucose Solution
The osmotic pressure of the glucose solution should be equal to the osmotic pressure of blood, which is given as 7.56 atm.
Step 2: Convert Osmotic Pressure to Pascal
To make the units compatible, we need to convert the osmotic pressure from atm to pascal (Pa). One atmosphere (atm) is equal to 101325 Pascal (Pa).
7.56 atm × 101325 Pa/atm = 765165 Pa
Step 3: Calculate the Molarity of Glucose Solution
The osmotic pressure is related to the molarity of the solution by the equation:
π = nRT
Where:
π is the osmotic pressure
n is the number of moles of solute (glucose)
R is the ideal gas constant (0.0821 L·atm/(mol·K))
T is the temperature in Kelvin (37 degrees Celsius = 310 K)
Rearranging the equation to solve for n (moles of glucose):
n = π / (RT)
n = 765165 Pa / (0.0821 L·atm/(mol·K) × 310 K)
n = 30.26 mol
Step 4: Convert Moles to Mass
The molecular weight of glucose is 180.16 g/mol.
Mass = moles × molecular weight
Mass = 30.26 mol × 180.16 g/mol
Mass = 5454.416 g or approximately 5454 g
So, approximately 5454 grams of glucose should be dissolved per liter of solution for an intravenous injection to be isotonic with blood.