a sucrose solution with a volume of B uL has a density of C g/ml. the solution is D % sucrose by mass. if i added x ml of this sucrose to another solution, how many grams sucrose did I add?a sucrose so
One can get very confused with all of the symbols; what I do is make up a problem, then substitute symbols.
Let's say we have a 10% sucrose soln that has a density of 1.1 g/mL (that may not be right but it doesn't matter since we're just doing the exercise to keep symbols straight) and we want to add 5 mL of it to a beaker. How much sucrose did we add?
10%soln means 10g/100 g soln.
If the density is 1.1 g/mL then 100 g soln has a volume of 100/1.1 = 90.9 mL. If we add 5 mL of that soln then we've added 10 g x (5 mL/90.9 mL) = 0.55 g sucrose. Done in one step that is
10 x 1.1 x (5/100) = 0.55 g sucrose.
So that is D%*density*x mL/100 = g sucrose added to the other beaker. I don't see that the B uL has anything to do with it--that's the amount of solution you have. Obviously B uL must be greater than the x mL that is being added; otherwise the x mL can't be added.
To determine the amount of sucrose added, we need to calculate the mass of the sucrose solution and then subtract the mass of the pure solvent.
Step 1: Calculate the mass of the sucrose solution.
Given:
Volume of the sucrose solution: B uL
Density of the sucrose solution: C g/ml
We can use the formula: mass = volume × density
Mass of the sucrose solution = B uL × (C g/ml)
Note: Ensure that the units are consistent. If necessary, convert units before calculation.
Step 2: Convert the volume of sucrose solution to grams.
Since we know the density of the sucrose solution, we can convert the volume from microliters (uL) to grams (g) by using the formula:
1 mL = 1 g
So, we can convert B uL to grams by dividing B by 1000:
Volume of the sucrose solution in grams = B uL / 1000
Step 3: Calculate the mass of the added sucrose.
Given:
Volume of sucrose added: x mL
Similarly, we can convert the volume added to grams:
Mass of added sucrose = x mL / 1000
Therefore, the amount of sucrose added is the difference between the mass of the sucrose solution and the mass of the pure solvent:
Amount of added sucrose = Mass of the sucrose solution - Mass of the pure solvent
= (B uL × C g/ml) - (B uL / 1000)
Note: Ensure that the units of each term are consistent.
I hope this explanation helps you understand how to calculate the amount of sucrose added to another solution!