Analysis of a gaseous organic compound gave 40% carbon and 6.7% hydrogen.0.010g of it occupied 8.15c.c. At 298k and 760 mm. What is the molecular formula

To determine the molecular formula of the gaseous organic compound, we need to follow a systematic approach that involves calculating the empirical formula first and then using the molar mass to find the molecular formula. Let’s break this down step by step.

Step 1: Determine the Empirical Formula

We start with the percentage composition of the compound, which is given as 40% carbon (C) and 6.7% hydrogen (H). To find the empirical formula, we need to convert these percentages into moles.

• Carbon: The molar mass of carbon is approximately 12 g/mol. Therefore, the number of moles of carbon in 40 g is:

Number of moles of C = 40 g / 12 g/mol = 3.33 moles

• Hydrogen: The molar mass of hydrogen is about 1 g/mol. Thus, the number of moles of hydrogen in 6.7 g is:

Number of moles of H = 6.7 g / 1 g/mol = 6.7 moles

Next, we need to find the simplest whole number ratio of moles of carbon to moles of hydrogen. We can do this by dividing each by the smallest number of moles:

• For carbon: 3.33 / 3.33 = 1
• For hydrogen: 6.7 / 3.33 ≈ 2.01

This gives us a ratio of approximately 1:2, leading us to the empirical formula of CH₂.

Step 2: Calculate the Molar Mass of the Compound

Next, we need to find the molar mass of the compound using the ideal gas law, which 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 that the pressure is 760 mmHg (which is equivalent to 1 atm), the volume is 8.15 c.c. (or 0.00815 L), and the temperature is 298 K, we can rearrange the equation to solve for n (the number of moles):

n = PV / RT

Substituting the known values:

n = (1 atm * 0.00815 L) / (0.0821 L·atm/(K·mol) * 298 K) ≈ 0.00033 moles

Step 3: Calculate the 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 4: Determine the Molecular Formula

Now that we have the empirical formula (CH₂) and the molar mass (approximately 30.3 g/mol), we can find the molecular formula. The molar mass of the empirical formula CH₂ is:

Molar mass of CH₂ = 12 g/mol (C) + 2 g/mol (H) = 14 g/mol

To find the ratio of the molar mass of the compound to the molar mass of the empirical formula:

Ratio = Molar mass of compound / Molar mass of empirical formula = 30.3 g/mol / 14 g/mol ≈ 2.16

Since we need a whole number, we round this to 2. Thus, the molecular formula is:

CH₂ × 2 = C₂H₄

Final Result

The molecular formula of the gaseous organic compound is C₂H₄, which is commonly known as ethylene.