Question

A 1.17 g sample of an alkane hydrocarbon gas occupies a volume of 674 mL at 28°C and 741 mmHg. Alkanes are known to have the general formula C nH 2n+2. What is the molecular formula of the gas in this sample? (R = 0.08206 L×atm/K×mol)

Answer 1

To find the molecular formula of the alkane hydrocarbon gas, we can use the ideal gas law to calculate the number of moles of the gas. By dividing the mass of the gas sample by the number of moles, we can determine the molar mass and molecular formula. In this case, the molecular formula is C8H18.

Step-by-step explanation:

The general formula for an alkane is CnH2n+2. Given that the alkane hydrocarbon gas sample has a mass of 1.17 g and occupies a volume of 674 mL at 28°C and 741 mmHg, we can use the ideal gas law to find the number of moles of the gas. The ideal gas law is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. Rearranging the equation, we have n = PV / RT. Converting the temperature to Kelvin (28°C + 273.15), pressure to atm (741 mmHg / 760 mmHg/atm), and volume to liters (674 mL / 1000 mL/L), we can calculate the number of moles. Then, using the molar mass of the gas (mass / moles), we can determine the molecular formula. In this case, the molecular formula of the gas is C8H18.

Answer 2

C3H8

Step-by-step explanation:

Step 1:

Data obtained from the question. This includes the following:

Mass of alkane = 1.17g

Volume (V) = 674 mL

Temperature (T) = 28°C

Pressure (P) = 741 mmHg.

Gas constant (R) = 0.08206 atm.L/Kmol

Step 2:

Conversion to appropriate unit.

For Volume:

1000mL = 1L

Therefore, 674mL = 674/1000 = 0.674L

For Temperature:

Temperature (Kelvin) = Temperature (celsius) + 273

Temperature (celsius) = 28°C

Temperature (Kelvin) = 28°C + 273 = 301K

For Pressure:

760mmHg = 1atm

Therefore, 741 mmHg = 741/760 = 0.975atm

Step 3:

Determination of the number of mole of the alkane..

The number of mole of the alkane can be obtained by using the ideal gas equation. This is illustrated below:

Volume (V) = 0.674L

Temperature (T) = 301K

Pressure (P) = 0.975atm

Gas constant (R) = 0.08206 atm.L/Kmol

Number of mole (n) =?

PV = nRT

n = PV /RT

n = (0.975 x 0.674)/(0.08206x301)

n = 0.0266 mole

Step 4:

Determination of the molar mass of the alkane.

Mass of alkane = 1.17g

Number of mole of the alkane = 0.0266mole

Molar Mass of the alkane =?

Number of mole = Mass/Molar Mass

Molar Mass = Mass/number of mole

Molar Mass of the alkane = 1.17/0.0266 = 44g/mol

Step 5:

Determination of the molecular formula of the alkane.

This is illustrated below:

The general formula for the alkane is CnH2n+2

To obtain the molecular formula for the alkane we shall assume n = 1, 2, 3 or more till we arrive at molar Mass of 44.

When n = 1

CnH2n+2 = CH4 = 12 + (4x1) = 16g/mol

When n = 2

CnH2n+2 = C2H6 = (12x2) + (6x1) = 30g/mol

When n = 3

CnH2n+2 = C3H8 = (12x3) + (8x1) = 44g/mol

We can see that when n is 3, the molar mass is 44g/mol.

Therefore, the molecular formula for the alkane is C3H8.