1) At body temperature of 36.5 ° C the osmotic pressure of the blood is of 7.80 atm. Calculate the mass of glucose (C6H12O6) that must be added to one liter of a solution containing 5 g / L of NaCl to be able to inject directly into a vein.
To calculate the mass of glucose that must be added to the solution, we need to determine the concentration of glucose required to reach the desired osmotic pressure.
First, let's calculate the osmotic pressure contributed by NaCl in the solution. The formula to calculate osmotic pressure (𝜋) is:
𝜋 = MRT
Where:
𝜋 = osmotic pressure
M = molarity of the solute
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin
Given that the osmotic pressure is 7.80 atm at a body temperature of 36.5 °C (which is 309.65 K), we can calculate the molarity of NaCl using the osmotic pressure formula:
7.80 atm = MNaCl * 0.0821 L·atm/(mol·K) * 309.65 K
Solving for MNaCl:
MNaCl = 7.80 atm / (0.0821 L·atm/(mol·K) * 309.65 K)
Next, we need to convert the given concentration of NaCl (5 g/L) to molarity. For that, we will need the molar mass of NaCl, which is 58.44 g/mol:
Molarity = Concentration / Molar mass
Converting 5 g/L to molarity:
MNaCl = 5 g/L / 58.44 g/mol
Now that we have the molarity of NaCl, we can determine the desired molarity of glucose (C6H12O6) needed to achieve the desired osmotic pressure in the solution. Glucose dissociates into particles of C6H12O6 when dissolved in the solution, so the molarity of glucose will be the same as the calculated molarity of NaCl:
MGlucose = MNaCl
Finally, we can calculate the mass of glucose required to be added to one liter of the solution. We'll first convert the desired molarity to moles:
Moles of glucose = MGlucose * Volume of solution
Since we want to add the glucose to one liter of the solution (1000 mL), we can now calculate the mass of glucose using its molar mass:
Mass of glucose = Moles of glucose * Molar mass of glucose
Using the molar mass of glucose (180.16 g/mol):
Mass of glucose = Moles of glucose * 180.16 g/mol
By following these steps, you can calculate the mass of glucose (C6H12O6) to be added to the given solution in order to obtain the desired osmotic pressure of 7.80 atm.