1. An organic compound with a formula mass of 417 g/mol was
analyzed for ethoxyl (CH3CH2O—) groups by the reactions
ROCH2CH3 + HI ROH + CH3CH2I
CH3CH2I + Ag+ + OH- AgI(s) + CH3CH2OH
A 25.42-mg sample of compound produced 29.03 mg of AgI. Howmany ethoxyl groups are there in each molecule?
417 x (29.03/25.42) = 476
476/235 = 2.02 rounds to 2 as a whole number so there are 2 of those groups present.
There is an easier way to do this, at least easier to understand I think. As follows:
mmols AgI = mg AgI/molar mass AgI = 29.03/235 = 0.124
You get 1 mmol AgI for every mmol of the CH3CH2O group. so you have 0.124 mmols of the ethoxy group.
molar mass of the group is 25.42/0.124 = about 205 so now
417/205 = 2.02 which rounds to 2 groups.
To determine the number of ethoxyl (CH3CH2O—) groups in each molecule, we need to find the number of moles of AgI produced and the number of moles of AgI per mole of ethoxyl group.
Given:
Formula mass of the organic compound = 417 g/mol
Mass of AgI produced = 29.03 mg
Mass of the sample = 25.42 mg
Step 1: Convert mass of AgI produced and sample to moles.
Molar mass of AgI = 126.9 g/mol
Moles of AgI = mass of AgI produced / molar mass of AgI
Moles of AgI = 29.03 mg / (126.9 g/mol * 1000 mg/g)
Moles of AgI = 0.0002283 mol
Moles of sample = mass of sample / molar mass of the organic compound
Moles of sample = 25.42 mg / (417 g/mol * 1000 mg/g)
Moles of sample = 0.00006098 mol
Step 2: Determine the ratio of moles of AgI to moles of ethoxyl group.
According to the second reaction, 1 mole of ethoxyl group reacts with 1 mole of AgI.
Ratio of moles of AgI to moles of ethoxyl group = 1:1
Step 3: Calculate the number of moles of ethoxyl group in each molecule.
Moles of ethoxyl group = moles of AgI * (moles of ethoxyl group / moles of AgI)
Moles of ethoxyl group = 0.0002283 mol * (1 mol / 1 mol)
Moles of ethoxyl group = 0.0002283 mol
Step 4: Calculate the number of ethoxyl groups in each molecule.
Number of ethoxyl groups = Moles of ethoxyl group * Avogadro's number
Number of ethoxyl groups = 0.0002283 mol * 6.022 x 10^23 mol^-1
Number of ethoxyl groups ≈ 1.375 x 10^20
Therefore, there are approximately 1.375 x 10^20 ethoxyl groups in each molecule.
To determine the number of ethoxyl (CH3CH2O—) groups in each molecule, we need to calculate the molar mass of ethoxyl and use it to find the number of moles of AgI produced.
First, let's calculate the molar mass of CH3CH2O—:
C (carbon) has a molar mass of 12.01 g/mol
H (hydrogen) has a molar mass of 1.01 g/mol
O (oxygen) has a molar mass of 16.00 g/mol
Molar mass of CH3CH2O— = (2 × C) + (6 × H) + O = (2 × 12.01) + (6 × 1.01) + 16.00 = 46.07 g/mol
Next, let's convert the given sample mass of the compound to moles using its molar mass:
Sample mass = 25.42 mg = 0.02542 g
Number of moles of the compound = Sample mass / Molar mass
Number of moles of the compound = 0.02542 g / 417 g/mol ≈ 0.000061 moles
Now, we need to find the number of moles of AgI produced. The molar ratio between AgI and CH3CH2O— is 1:1, since 1 mole of AgI is formed for each mole of CH3CH2O— reacted.
Number of moles of AgI = 0.000061 moles
Finally, we can calculate the number of ethoxyl groups by dividing the number of moles of AgI by the number of moles of CH3CH2O—:
Number of ethoxyl groups = Number of moles of AgI / Number of moles of CH3CH2O—
Number of ethoxyl groups = 0.000061 moles / 0.000061 moles = 1
Therefore, there is one ethoxyl group in each molecule of the organic compound.