A gaseous hydrogen and carbon containing compound is decomposed and found to contain 85.63% C and 14.37% H by mass. The mass of 258 mL of the gas, measured at STP, was found to be 0.646 g.What is the molecular formula of the compound?
a. Take a 100 g sample which gives you
85.63 g C and
14.37 g H.
Convert to mols.
85.63/12 = ?
14.37/1 = ?
Now find the ratio of C to H with the smaller number being 1.0 and round to whole numbers. This gives you the empirical formula.
b. Use PV = nRT and solve for n = number of mols. Then mol = grams/molar mass. You know mols and grams, solve for molar mass. )As an alternative, 22.4 L at STP will be 1 mol of the gas)
c. Calculate the empirical formula mass. It will be CxHy where x and y are the subscripts for the formula. Find the empirical formula mass. Then
(empirical formula)z = molar mass where z represents the number of formula units in the molecular formula. Round to a whole number for the molecular formula. Post your work if you get stuck.
Well, it looks like we have ourselves a gassy mystery here! Let me put on my detective nose and solve this case for you.
We know that the compound contains 85.63% carbon and 14.37% hydrogen by mass. So, let's assume we have 100 grams of this compound.
In that case, we would have 85.63 grams of carbon and 14.37 grams of hydrogen. Now let's convert these masses into moles.
The molar mass of carbon is approximately 12 grams/mol, so we have (85.63 g C) / (12 g/mol C) ≈ 7.14 moles of carbon.
The molar mass of hydrogen is approximately 1 gram/mol, so we have (14.37 g H) / (1 g/mol H) = 14.37 moles of hydrogen.
To find the empirical formula, we need to find the simplest ratio of carbon to hydrogen. And it looks like we have a ratio of approximately 1:2 (7.14 moles C to 14.37 moles H).
The next step is figuring out the molecular formula. To do this, we need the molar mass of the compound.
We have the mass of 0.646 grams of the compound and we know it occupies 258 mL, so we can use the molar volume at STP (22.4 L/mol) to find the molar mass.
(0.646 g) / ((258 mL) / (1000 mL/L)) * (22.4 L/mol) = 5.44 g/mol
Now, we need to find the ratio between the molar mass of the empirical formula and the molar mass of the compound.
Molar mass of the empirical formula:
(12 g/mol C) + 2 * (1 g/mol H) = 14 g/mol
Now, we divide the molar mass of the compound by the molar mass of the empirical formula to find the number of empirical formula units in one molecule of the compound.
5.44 g/mol ÷ 14 g/mol = 0.39
Since we can't have a fraction of a molecule, we round it off to the nearest whole number. So the empirical formula is C1H2.
That means the molecular formula of this compound is also C1H2.
So, it looks like the clown detective has cracked the case! The molecular formula of the compound is C1H2. Mystery solved! 🕵️♂️🎭
To determine the molecular formula of the compound, we need to find the empirical formula first. The empirical formula represents the simplest whole-number ratio of elements present in a compound.
Given:
- Percentage composition by mass: 85.63% C, 14.37% H
- Mass of 258 mL of the gas at STP: 0.646 g
Step 1: Convert percentages to grams
Assuming we have 100 g of the compound, we can calculate the masses of carbon (C) and hydrogen (H) present in the compound.
Mass of C = (85.63 / 100) * 100 g = 85.63 g
Mass of H = (14.37 / 100) * 100 g = 14.37 g
Step 2: Calculate the number of moles
To calculate the number of moles of each element, we need their molar masses. The molar mass of C is 12.01 g/mol, and the molar mass of H is 1.01 g/mol.
Moles of C = Mass of C / Molar mass of C = 85.63 g / 12.01 g/mol = 7.13 mol
Moles of H = Mass of H / Molar mass of H = 14.37 g / 1.01 g/mol = 14.23 mol
Step 3: Determine the empirical formula
To find the empirical formula, we divide the number of moles of each element by the smallest number of moles obtained.
Dividing by 7.13 (smallest mole value), we get approximately 1 C atom and 2 H atoms.
Empirical formula: CH2
Step 4: Determine the molecular formula
To determine the molecular formula, we need to know the molar mass of the compound. Since the mass of 258 mL of the gas was measured at STP, we can convert it into moles using the ideal gas law.
PV = nRT
P = pressure (STP = 1 atm)
V = volume (258 mL = 0.258 L)
n = moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (STP = 273 K)
Rearranging the equation: n = PV / RT
n = (1 atm)(0.258 L) / (0.0821 L·atm/(mol·K))(273 K) = 0.0101 mol
The molecular formula may be obtained by dividing the molar mass of the compound by the empirical formula mass (sum of the atomic masses of empirical formula atoms: C + 2H). The molar mass of CH2 is 14.03 g/mol.
Molar mass of compound = 0.646 g / 0.0101 mol = 63.96 g/mol
Dividing the molar mass of the compound by the molar mass of the empirical formula:
63.96 g/mol / 14.03 g/mol ≈ 4.56
The ratio 4.56 indicates that the empirical formula should be multiplied by 4. Therefore, the molecular formula is approximately 4(CH2), which simplifies to C4H8.
The molecular formula of the compound is C4H8.
To determine the molecular formula of the compound, we need to follow a step-by-step process.
Step 1: Calculate the number of moles of carbon (C) and hydrogen (H) in the compound.
To do this, assume we have 100 g of the compound. From the given percentages, we can calculate the mass of carbon (C) and hydrogen (H) in this 100 g sample:
- Mass of C = 85.63% of 100 g = 85.63 g
- Mass of H = 14.37% of 100 g = 14.37 g
Next, determine the number of moles of carbon (C) and hydrogen (H) using their respective molar masses. The molar mass of carbon (C) is 12.01 g/mol, and the molar mass of hydrogen (H) is 1.01 g/mol.
- Moles of C = Mass of C / Molar mass of C = 85.63 g / 12.01 g/mol = 7.13 mol
- Moles of H = Mass of H / Molar mass of H = 14.37 g / 1.01 g/mol = 14.23 mol
Step 2: Determine the empirical formula of the compound.
The empirical formula represents the simplest whole number ratio of atoms in a compound, so divide the number of moles of each element by the smallest number of moles to find the simplest ratio.
- Empirical ratio of C : H = 7.13 mol : 14.23 mol ≈ 0.5 : 1.0
- Multiplying by 2 to eliminate the decimal gives C : H = 1 : 2
Step 3: Determine the molecular formula of the compound.
The molecular formula represents the actual number of atoms in each element. To find the molecular formula, we need the molar mass of the compound. From the given information, we know the mass of 258 mL of the gas is 0.646 g at STP conditions.
To convert the mass of the gas to the number of moles, we use the ideal gas law:
PV = nRT
Where:
P = pressure
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (in Kelvin)
At STP, the pressure is 1 atm, and the volume is 258 mL, which is 0.258 L. The temperature is 273 K.
Solving for n:
(1 atm)(0.258 L) = (n)(0.0821 L.atm/mol.K)(273 K)
n = (1 atm)(0.258 L) / (0.0821 L.atm/mol.K)(273 K)
n ≈ 0.0099 mol
Now we have the number of moles of the compound present in the given mass. Let's call this number of moles "m."
The molecular formula will be a multiple of the empirical formula, so we need to find the whole number multiple:
Molecular formula = (Empirical formula) × (m / empirical formula mass)
First, we calculate the empirical formula mass by summing the atomic masses of the empirical formula. The empirical formula is CH2 (1C + 2H).
Empirical formula mass = 1(12.01 g/mol) + 2(1.01 g/mol) = 14.03 g/mol
Now, calculate the whole number multiple:
Molecular formula = (CH2) × (0.0099 mol / 14.03 g/mol)
Molecular formula ≈ (CH2) × 0.000705 mol/g
Finally, convert this to the simplest whole number ratio by dividing by the decimal value (0.000705 in this case).
The simplest whole number ratio of the molecular formula is approximately C1H2.
Therefore, the molecular formula of the compound is CH2.