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?
pi = MRT
7.56 = M*0.08205**273 + 37)
From M, then moles = grams/molar mass
thats what i did and i got it wrong. my answer was 53.46. the study guide says 54.2.
My answer is 53.5 grams. You have too many significant figures. The study guide must be wrong.
I got approx. 54.
Same set up. But the numbers I used were .08206 and MW = 180. and I got 54.
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 consider the concept of osmotic pressure.
Osmotic pressure is the pressure required to prevent the movement of solvent molecules across a semipermeable membrane, which occurs due to a difference in solute concentration. In this case, we want the osmotic pressure of the glucose solution to match that of blood.
Given that the osmotic pressure of blood at 37 degrees is 7.56 atm, we can use the following equation:
π = i * M * R * T
Where:
π represents the osmotic pressure,
i is the van't Hoff factor,
M is the molar concentration of the solute (in this case, glucose),
R is the ideal gas constant (0.0821 L * atm / (mol * K)),
T is the temperature in Kelvin (37 degrees Celsius = 310 Kelvin).
The van't Hoff factor (i) for glucose is 1, as it does not dissociate into ions in solution.
Rearranging the equation to solve for M (molar concentration) and substituting the given values, we get:
M = π / (i * R * T)
M = 7.56 atm / (1 * 0.0821 L * atm / (mol * K) * 310 K)
Now, the molecular weight (MW) of glucose is 180.16 g/mol. Since molar concentration (M) is calculated in mol/L, we can convert it to grams per liter (g/L) by multiplying it by the molecular weight:
Mass of glucose = M * MW
Substituting the calculated value of M into the equation, we can find the mass of glucose required per liter of solution:
Mass of glucose = (7.56 atm / (1 * 0.0821 L * atm / (mol * K) * 310 K)) * 180.16 g/mol
Evaluating this expression will give you the mass of glucose that should be dissolved per liter of solution for an intravenous injection to be isotonic with blood.