Askiitians Tutor Team
Last Activity: 18 Hours ago
To determine the molecular formula of the gaseous organic compound based on the provided data, we need to follow a systematic approach. We'll start by calculating the empirical formula using the percentage composition of carbon and hydrogen, then find the molar mass of the compound using the ideal gas law, and finally derive the molecular formula.
Step 1: Calculate Moles of Carbon and Hydrogen
The compound consists of 40% carbon and 6.7% hydrogen. To find the simplest ratio, we first assume we have 100 grams of the compound. This means we have:
- 40 grams of carbon (C)
- 6.7 grams of hydrogen (H)
Next, we convert these masses into moles:
- Moles of carbon = 40 g / 12.01 g/mol = 3.32 moles
- Moles of hydrogen = 6.7 g / 1.008 g/mol = 6.64 moles
Step 2: Determine the Empirical Formula
Now, we need to find the simplest whole number ratio of moles of carbon to moles of hydrogen:
- Ratio of C to H = 3.32 : 6.64
Dividing both by the smaller number (3.32):
- C: 3.32 / 3.32 = 1
- H: 6.64 / 3.32 = 2
This gives us an empirical formula of CH2.
Step 3: Calculate the Molar Mass of the Compound
Next, we will use the ideal gas law to find the molar mass. The ideal gas law is expressed as:
PV = nRT
Where:
- P = pressure in atm
- V = volume in liters
- n = number of moles
- R = ideal gas constant (0.0821 L·atm/(K·mol))
- T = temperature in Kelvin
Given:
- Pressure (P) = 760 mmHg = 1 atm
- Volume (V) = 8.15 c.c. = 0.00815 L
- Temperature (T) = 298 K
Now, we can rearrange the ideal gas law to solve for n (number of moles):
n = PV / RT
Substituting the values:
n = (1 atm * 0.00815 L) / (0.0821 L·atm/(K·mol) * 298 K)
n ≈ 0.00033 moles
Step 4: Calculate Molar Mass
Now, we can find the molar mass (M) of the compound using the mass and the number of moles:
M = mass / n
Given that the mass of the compound is 0.010 g:
M = 0.010 g / 0.00033 moles ≈ 30.3 g/mol
Step 5: Determine the Molecular Formula
Now we compare the molar mass we calculated with the molar mass of the empirical formula (CH2):
- Molar mass of CH2 = 12.01 g/mol + (2 * 1.008 g/mol) = 14.026 g/mol
Next, we find the ratio of the molar mass of the compound to the molar mass of the empirical formula:
Ratio = 30.3 g/mol / 14.026 g/mol ≈ 2.16
Since we round this to the nearest whole number, we get 2. Therefore, the molecular formula is:
C2H4.
Final Result
The molecular formula of the gaseous organic compound is C2H4, which is commonly known as ethylene.