The intravenous dosage of mannitol is 1.5g/kg, administered as a 15% mv solution. How many ml of the solution should be administered to a person with a body mass of 85kg?
How many grams mannitol do you need for an 85 kg person? That will be 85 kg x (1.5 g mannitol/1 kg) = ?? g mannitol. Note how the kg unit cancels to leave unit of g mannitol. Then, you have a 15% m/v solution. That is 15 g mannitol/100 mL solution.
127.5 g mannitol x (100 mL/15 g mannitol) = ??mL. Again, note g mannitol cancels to leave the unit you want which is mL.
850mL
682mL
To determine the dosage in milliliters, we need to calculate the total amount of mannitol needed based on the person's body mass and the concentration of the solution.
Step 1: Calculate the total amount of mannitol needed.
The intravenous dosage of mannitol is given as 1.5g/kg for this particular person with a body mass of 85kg.
Thus, the total amount of mannitol needed can be calculated as:
Total Mannitol = Body Mass (kg) x Dosage (g/kg)
Total Mannitol = 85kg x 1.5g/kg
Step 2: Calculate the volume of the solution to be administered.
The solution is given as a 15% mass/volume (mv) solution. This means that for every 100 ml of the solution, there is 15g of mannitol.
To calculate the volume of the solution needed, we set up a proportion:
(15g/100ml) = (Total Mannitol)/(x ml)
Cross-multiplying and solving for x, the volume of the solution needed:
15g * x ml = Total Mannitol * 100ml
x ml = (Total Mannitol * 100ml) / 15g
Now, let's substitute the value of Total Mannitol we calculated in Step 1:
x ml = (127.5g * 100ml) / 15g
Step 3: Calculate the volume of the solution needed in milliliters.
Simplifying the equation, we have:
x ml = 850 ml
Therefore, the person with a body mass of 85kg should receive 850 ml of the 15% mannitol solution intravenously.