Analysis of gaseous organic compound gave 40% carbon and 6.7% hydrogen.0.010g of it occupied 8.15c.c. at 298K and 760mm. what is the molecular formula?

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.

Approved