A student placed 14.0g of glucose (C6H1206) in a volumetric flask, added enough water to dissolve the glucose by swirling, then carefully added additional water until the 100.-mL mark on the neck of the flask was reached. The flask was then shaken until the solution was uniform. A 35.0-mL sample of this glucose solution was diluted to 0.500mL . How many grams of glucose are in 100mL. of the final solution?
To find the amount of glucose in the final solution, we need to calculate the concentration (in grams per milliliter) of the original glucose solution. We can then use this concentration to determine the grams of glucose in 100 mL of the final solution.
1. First, let's calculate the concentration of the original glucose solution:
Concentration (in g/mL) = Mass of glucose (in g) / Volume of solution (in mL)
Given:
Mass of glucose = 14.0 g
Volume of solution = 100 mL
Concentration = 14.0 g / 100 mL
Concentration = 0.14 g/mL
2. Now, let's calculate the amount of glucose in the 35 mL sample that was taken from the original solution:
Amount of glucose in 35mL of original solution = Concentration * Volume of sample
Given:
Concentration = 0.14 g/mL
Volume of sample = 35 mL
Amount of glucose = 0.14 g/mL * 35 mL
Amount of glucose = 4.9 g
3. Finally, to determine the grams of glucose in 100 mL of the final solution, we need to dilute the sample:
Given:
Initial volume of sample = 35 mL
Final volume of solution = 100 mL
Amount of glucose in sample = 4.9 g
We can set up a proportion to find the amount of glucose in 100 mL of the final solution:
Amount of glucose in 35 mL / Initial volume of sample = Amount of glucose in 100 mL / Final volume of solution
4.9 g / 35 mL = Amount of glucose in 100 mL / 100 mL
Cross-multiplying, we get:
(4.9 g)(100 mL) = (35 mL)(Amount of glucose in 100 mL)
Amount of glucose in 100 mL = (4.9 g)(100 mL) / 35 mL
Amount of glucose in 100 mL = 14 g
Therefore, there are 14 grams of glucose in 100 mL of the final solution.
To calculate the number of grams of glucose in 100 mL of the final solution, we need to perform a series of calculations.
First, let's determine the concentration of glucose in the 35.0 mL sample. We are told that this sample was diluted to 0.500 mL, so we can set up a dilution equation using the formula:
C1V1 = C2V2
Where:
C1 = initial concentration
V1 = initial volume
C2 = final concentration
V2 = final volume
We want to solve for C2, the concentration of the 35.0 mL sample:
C1 = ?
V1 = 35.0 mL
C2 = 0.500 mL
V2 = 100.0 mL (since we want to find the concentration in 100 mL)
Since we know that the initial concentration of glucose, C1, is equal to the concentration in the 14.0 g glucose solution, we can determine its value using the formula:
C = n/V
Where:
C = concentration in g/mL
n = moles of solute
V = volume in mL
The molar mass of glucose (C6H12O6) = (12.01 * 6) + (1.008 *12) + (16.00 *6) = 180.18 g/mol.
To calculate n, the number of moles of glucose in the 14.0 g sample, we divide the mass by the molar mass:
n = 14.0 g / 180.18 g/mol ≈ 0.07762 mol
Now that we have n, we can calculate the initial concentration:
C1 = n / V1 = 0.07762 mol / 35.0 mL = 0.00222 mol/mL
Using the dilution equation, we can find the final concentration (C2):
C1V1 = C2V2
(0.00222 mol/mL)(35.0 mL) = C2(0.500 mL)
C2 ≈ 0.00003171 mol/mL (or, equivalently, M)
Finally, to find the number of grams of glucose in 100 mL of the final solution, we multiply the concentration by the volume:
grams of glucose = C2 * V2
= 0.00003171 mol/mL * 100.0 mL
≈ 0.003171 mol * 180.18 g/mol
≈ 0.5714 g
Therefore, there are approximately 0.5714 grams of glucose in 100 mL of the final solution.
SURELY you have a typo. I don't know how you can dilute a 35.0 mL sample to 0.500 mL. You might dilute it to 0.500 L but not mL. I will assume you intended to write "A 35.0 mL sample of this glucose solution was diluted to 0.500 L. How many grams of glucose are in 100 mL of the final solution?"
These dilution problem really are simple if you just reason through them.
We have 14.0 g glucose in 100 mL. So that is 14.0/100 = 0.140 g/mL. Now we take a 35.0 mL sample of that solution. How much did we take? We have 0.14 g/mL x 35.0 mL = 4.90 g. We place that in a 0.500 L (500 mL) flask so now we have 4.90 g in 500 mL. How much is that per mL? 4.90/500 = 0.00980 g/mL. So how much is in 100 mL of that solution.
0.00980 x 100 = 0.980 grams/100 mL.
Check my thinking. Check my arithmetic.