A compound with the molar mass of approximately 142 g/mol has the composition 50.7% C, 9.9% H, and 39.4% N. What is its molecular formula?

Element order CxHyNz.

50.7% C, 9.9% H, and 39.4% N. If you take a 100 g sample you will have

50.7 g C, 9.9 g H and 39.4 g N.
mols C = 50.7/12 = about 4.2 but you can use more exact numbers here and below
mols H = 9.9/1 = 9.9
mols N = 39.4/14 = 2.8
To find the ratio divide by the smallest number. like this.
4.2/2.8 = 1.5 C
9.9/2.8 = 3.5 H
2.8/2.8 = 1.0 N
Since compounds are formed with WHOLE numbers and not fractions, convert them to whole numbers but keep the ratio the same. You can do that by multiplying each by 2 so you get 3 C, 7 H, and 2 N so the empirical formula is
C3H7N2 and the empirical mass will be 3*12 + 7*1 + 2*14 = 71
Then as I showed you below (C3H7N2)x = 142 which makes (71)x = 142 and x will be 2. The molecular formula then can be written as C6H14N4. I always like to check the molar mass to see that it is close to that 142.
6*12 = 72
14*1 = 14
4*14 = 56
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total = 142

Well, let's solve it with a bit of chemistry and a pinch of humor, shall we? Let's break it down, molecule-style!

To find the molecular formula, we need to determine the ratio of atoms in the compound. So, let's assume we have one mole of this mystery compound. That would give us 50.7 grams of carbon, 9.9 grams of hydrogen, and 39.4 grams of nitrogen.

Now, we need to convert those grams to moles. The molar mass of carbon is roughly 12 g/mol, hydrogen is about 1 g/mol, and nitrogen is approximately 14 g/mol. Dividing the given masses by the corresponding molar masses, we find that we have 4.225 moles of carbon, 9.9 moles of hydrogen, and 2.814 moles of nitrogen.

Next, we need to simplify this ratio by dividing each number by the smallest number of moles. In this case, the smallest number of moles is 2.814, which is the number of moles of nitrogen.

So, dividing the mole values by 2.814, we get approximately 1.5 moles of carbon, 3.5 moles of hydrogen, and 1 mole of nitrogen. Rounded to the nearest whole number, that gives us a ratio of 3:7:4.

And there you have it! The molecular formula of this mysterious compound is C3H7N4. Ta-da! It's time for a standing ovation for our famous molecule, the C3H7N4. Bravo, bravo!

To find the molecular formula of the compound, we need to determine the empirical formula first. The empirical formula represents the simplest whole number ratio of atoms present in a compound.

Step 1: Convert the percentages to grams.
Assume we have 100 grams of the compound.
- 50.7% C = 50.7 grams
- 9.9% H = 9.9 grams
- 39.4% N = 39.4 grams

Step 2: Determine the moles of each element.
To find the number of moles, divide the mass of each element by its molar mass.
- Moles of C = 50.7g / 12.01 g/mol = 4.22 mol
- Moles of H = 9.9g / 1.01 g/mol = 9.8 mol
- Moles of N = 39.4g / 14.01 g/mol = 2.81 mol

Step 3: Divide the number of moles by the smallest value.
Finding the smallest whole-number ratio helps us determine the empirical formula.
- Divide the moles of each element by the smallest number of moles (in this case, 2.81).

- C = 4.22 mol / 2.81 = 1.50 (approximately)
- H = 9.80 mol / 2.81 = 3.49 (approximately)
- N = 2.81 mol / 2.81 = 1.00

Step 4: Round off the ratios to the nearest whole number.
The empirical formula is found by taking the closest whole number ratio of the elements.
- C ≈ 1.50 ≈ 2
- H ≈ 3.49 ≈ 4
- N = 1.00

Therefore, the empirical formula is C2H4N.

Step 5: Calculate the molecular formula.
The molar mass of the empirical formula (C2H4N) can be calculated as follows:
(2 * molar mass of C) + (4 * molar mass of H) + (molar mass of N)
= (2 * 12.01 g/mol) + (4 * 1.01 g/mol) + (14.01 g/mol)
= 24.02 g/mol + 4.04 g/mol + 14.01 g/mol
= 42.07 g/mol

The molecular formula is determined by comparing the molar mass of the empirical formula to the given molar mass of 142 g/mol.
If the molar mass of the empirical formula is a fraction of the given molar mass, then multiply the subscripts of the empirical formula by that fraction to obtain the molecular formula.

Molar mass of empirical formula = 42.07 g/mol
Given molar mass = 142 g/mol

Molar mass ratio = Given molar mass / Molar mass of empirical formula
= 142 g/mol / 42.07 g/mol
= 3.38

Multiply the subscripts of the empirical formula by 3.38 to obtain the molecular formula:
C2H4N * 3.38 = C6.76H13.52N3.38

Rounding off to the nearest whole numbers, the molecular formula is C7H14N3.

To find the molecular formula of the compound, we need to determine the empirical formula first. The empirical formula represents the simplest whole-number ratio of atoms in a compound.

1. Start by assuming we have 100 grams of the compound. Then, convert the percentages into grams for each element:
- 50.7% of 100g = 50.7g C
- 9.9% of 100g = 9.9g H
- 39.4% of 100g = 39.4g N

2. Next, determine the moles of each element by dividing the mass (grams) of each element by their molar masses:
- Moles of C = 50.7g / atomic mass of C
- Moles of H = 9.9g / atomic mass of H
- Moles of N = 39.4g / atomic mass of N

3. The molar masses of carbon (C), hydrogen (H), and nitrogen (N) are approximately 12 g/mol, 1 g/mol, and 14 g/mol, respectively.

4. Calculate the moles of each element:
- Moles of C = 50.7g / 12 g/mol ≈ 4.23 mol C
- Moles of H = 9.9g / 1 g/mol ≈ 9.9 mol H
- Moles of N = 39.4g / 14 g/mol ≈ 2.81 mol N

5. Find the simplest whole-number ratio by dividing each number of moles by the smallest number of moles. In this case, 2.81 mol N is the smallest number of moles.

- Divide the number of moles of each element by 2.81 mol:
- Carbon: 4.23 mol C / 2.81 mol = 1.5 (approximated to nearest whole number)
- Hydrogen: 9.9 mol H / 2.81 mol = 3.52 (approximated to nearest whole number)
- Nitrogen: 2.81 mol N / 2.81 mol = 1 (since it's already the smallest)

6. Use the whole-number ratio obtained to write the empirical formula of the compound: C1.5H3.52N1 (simplified to C3H7N2).

7. Finally, to determine the molecular formula, we need to know the molar mass of the compound. In this case, it's given as approximately 142 g/mol.

8. Calculate the empirical formula's molar mass by adding up the molar masses of the elements:
- Molar mass of C = 12 g/mol
- Molar mass of H = 1 g/mol
- Molar mass of N = 14 g/mol

- Empirical formula molar mass = (12 g/mol x 3) + (1 g/mol x 7) + (14 g/mol x 2)
- Empirical formula molar mass = 36 g/mol + 7 g/mol + 28 g/mol
- Empirical formula molar mass = 71 g/mol

9. Determine the molecular formula by dividing the given molar mass by the empirical formula molar mass:
- Molecular formula molar mass = 142 g/mol / 71 g/mol = 2

10. Multiply the empirical formula by the molecular formula molar mass to obtain the molecular formula:
- Molecular formula = (C3H7N2) x 2
- Molecular formula = C6H14N4

Therefore, the molecular formula of the compound is C6H14N4.