Alcohol levels in blood can be determined by a redox titration with potassium dichromate according to the balanced equation:
C2H5OH(aq) +2Cr2O7-2 (aq) + 16H+(aq)---> 2CO2 (g) + 4 Cr3+ (aq) + 11H2O (l)
What is the blood alcohol level in mass perecent if 8.76 mL of 0.04988 M K2Cr2O7 is required for titration of a 10.0002 g sample of blood?
moles Cr2O7^-2 = M x L = ??
Convert mole Cr2O7^-2 to moles C2H5OH using the coefficients in the balanced equation. That will be
moles Cr2O7^-2 x (1 mole C2H5OH/2 moles Cr2O7^-2) = ??moles x (1/2) = xx moles C2H5OH.
g C2H5OH = moles C2H5OH x molar mass C2H5OH.
%C2H5OH = (g C2H5OH/mass sample)*100 = ??
To find the blood alcohol level in mass percent, we need to determine the amount of alcohol present in the blood sample and then calculate its percentage relative to the total mass.
Here's how you can solve it step-by-step:
Step 1: Convert the volume of K2Cr2O7 solution to moles.
The molarity (M) of K2Cr2O7 is given as 0.04988 M.
Using the equation M = moles/volume (in L), we can calculate the number of moles:
moles K2Cr2O7 = M × volume (in L)
Given volume = 8.76 mL = 8.76 × 10^-3 L
moles K2Cr2O7 = 0.04988 M × 8.76 × 10^-3 L
Step 2: Determine the number of moles of ethanol (C2H5OH) in the blood sample.
From the balanced chemical equation, we can see that the ratio between K2Cr2O7 and C2H5OH is 1:1.
Therefore, moles C2H5OH = moles K2Cr2O7
Step 3: Calculate the molar mass of C2H5OH.
C: 12.01 g/mol
H: 1.01 g/mol (× 6 since there are six hydrogen atoms in ethanol)
O: 16.00 g/mol
Molar mass C2H5OH = 2(12.01) + 6(1.01) + 16.00 = 46.07 g/mol
Step 4: Convert the mass of the blood sample to moles of ethanol.
mass of blood sample = 10.0002 g
moles C2H5OH = mass (in g) / molar mass (in g/mol)
Step 5: Calculate the blood alcohol level in mass percent.
Mass percent = (mass of ethanol / total mass of blood sample) × 100
We can now substitute the given values in Step 1 to Step 4 into the final step:
Mass percent = (moles C2H5OH × molar mass C2H5OH / mass of blood sample) × 100
Note: In this calculation, it is assumed that the given volume of K2Cr2O7 solution is the exact volume required for complete reaction with ethanol in the blood sample.
To determine the blood alcohol level in mass percent, we first need to calculate the number of moles of potassium dichromate used in the titration.
Step 1: Convert the volume of the potassium dichromate solution into moles.
Moles = Volume (L) × Concentration (mol/L)
Given:
Volume = 8.76 mL = 8.76/1000 L = 0.00876 L
Concentration = 0.04988 M
Moles of K2Cr2O7 = 0.00876 L × 0.04988 mol/L = 4.361 × 10^-4 mol
Step 2: Use the balanced equation to determine the moles of ethanol (C2H5OH) in the blood sample.
According to the balanced equation:
1 mole of C2H5OH reacts with 2 moles of K2Cr2O7
Therefore:
Moles of C2H5OH = (Moles of K2Cr2O7) ÷ 2 = (4.361 × 10^-4 mol) ÷ 2 = 2.181 × 10^-4 mol
Step 3: Calculate the mass of ethanol (C2H5OH) in the blood sample.
Molar mass of C2H5OH = 2 × (12.01 g/mol) + 6 × (1.01 g/mol) + 1 × (16.00 g/mol)
= 46.07 g/mol
Mass of C2H5OH = (Moles of C2H5OH) × (Molar mass of C2H5OH)
= (2.181 × 10^-4 mol) × (46.07 g/mol)
≈ 0.01004 g
Step 4: Calculate the blood alcohol level in mass percent.
Blood Alcohol Level (mass percent) = (Mass of ethanol / Mass of blood sample) × 100
Given:
Mass of blood sample = 10.0002 g
Blood Alcohol Level (mass percent) = (0.01004 g / 10.0002 g) × 100
≈ 0.1004%
Therefore, the blood alcohol level in mass percent is approximately 0.1004%.