During a Breathalyzer Test it was determined that 1.60mg of K2Cr2O7 was consumed by the above reaction. Calculate the number of milligrams of ethanol in the test sample.
2K2Cr2O7 + 8H2SO4 + 3C2H5OH → 2Cr2(SO4)3 + 2K2SO4 + 3CH3COOH + 11H2O
Convert 1.60 mg K2Cr2O7 to mg C2H5OH as follows:
mols K2Cr2O7 = 0.00160/molar mass K2Cr2O7.
Using the coefficients in the balanced equation, convert mols K2Cr2O7 to mols C2H5OH. That's mols K2Cr2O7 from above x (3 mols C2H5OH/2 mols K2Cr2O7) = mols K2Cr2O7 from above x (3/2) = ?
Then grams C2H5OH = mols C2H5OH x molar mass C2H5OH and convert g to mg.
To calculate the number of milligrams of ethanol in the test sample, we need to use the balanced chemical equation for the reaction between ethanol and K2Cr2O7.
The balanced chemical equation is as follows:
3C2H5OH + 2K2Cr2O7 + 8H2SO4 -> 3CH3COOH + 2Cr2(SO4)3 + 2K2SO4 + 11H2O
Based on the equation, we can see that for every 3 moles of ethanol (C2H5OH), we need 2 moles of K2Cr2O7.
Using the molar mass of K2Cr2O7, which is approximately 294.19 g/mol, and the given amount of K2Cr2O7, 1.60 mg, we can calculate the number of moles of K2Cr2O7 consumed:
1.60 mg / 294.19 g/mol = 0.00544 mol
Since the stoichiometric ratio between ethanol and K2Cr2O7 is 3:2, we can calculate the moles of ethanol consumed by multiplying the moles of K2Cr2O7 by (3/2):
0.00544 mol * (3/2) = 0.00816 mol
Now, we need to convert the moles of ethanol into milligrams. The molar mass of ethanol (C2H5OH) is approximately 46.07 g/mol:
0.00816 mol * 46.07 g/mol = 0.375 mg
Therefore, there are approximately 0.375 milligrams of ethanol in the test sample.
To calculate the number of milligrams of ethanol in the test sample, we need to understand the reaction taking place in the Breathalyzer Test.
In the given question, K2Cr2O7 is likely being used as the oxidizing agent to react with ethanol (C2H5OH). The balanced chemical equation for this reaction is:
3 C2H5OH + 2 K2Cr2O7 + 8 H2SO4 → 3 CH3COOH + 4 Cr2(SO4)3 + 2 K2SO4 + 11 H2O
From the balanced equation, we can see that it takes three moles of ethanol to react with two moles of K2Cr2O7. So we need to determine the number of moles of K2Cr2O7 consumed first.
Given: 1.60 mg of K2Cr2O7
To convert milligrams to moles, we need to know the molar mass of K2Cr2O7. Adding up the atomic masses of all the atoms in K2Cr2O7, we get:
Molar mass of K2Cr2O7 = (2 * molar mass of K) + (2 * molar mass of Cr) + (7 * molar mass of O)
Molar mass of K2Cr2O7 = (2 * 39.10 g/mol) + (2 * 52.00 g/mol) + (7 * 16.00 g/mol)
Molar mass of K2Cr2O7 = 294.20 g/mol
Now we can calculate the number of moles of K2Cr2O7 consumed:
Number of moles = mass / molar mass
Number of moles = 1.60 mg / 294.20 g/mol
Number of moles = 0.00544 mol (rounded to five decimal places)
According to the balanced equation, every 2 moles of K2Cr2O7 react with 3 moles of C2H5OH. Therefore, we need to find the number of moles of C2H5OH consumed:
Number of moles of C2H5OH = (3 moles C2H5OH / 2 moles K2Cr2O7) * 0.00544 mol
Number of moles of C2H5OH = 0.00816 mol (rounded to five decimal places)
Finally, to calculate the mass of ethanol consumed, we multiply the number of moles by the molar mass of ethanol.
Molar mass of C2H5OH = (2 * molar mass of C) + (6 * molar mass of H) + (1 * molar mass of O)
Molar mass of C2H5OH = (2 * 12.01 g/mol) + (6 * 1.008 g/mol) + (1 * 16.00 g/mol)
Molar mass of C2H5OH = 46.07 g/mol
Mass of ethanol consumed = number of moles * molar mass of C2H5OH
Mass of ethanol consumed = 0.00816 mol * 46.07 g/mol
Mass of ethanol consumed = 0.3757 g (rounded to four decimal places)
Therefore, the number of milligrams of ethanol in the test sample is 375.7 mg (rounded to one decimal place).