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Ludmilka
2 months ago
14

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 gen

eral formula C nH 2n+2. What is the molecular formula of the gas in this sample? (R = 0.08206 L×atm/K×mol)
Computers and Technology
1 answer:
Natasha_Volkova [1K]2 months ago
7 0

Answer:

C3H8

Explanation:

Step 1:

Relevant details from the question are noted below:

Mass of the alkane is 1.17g

Volume (V) = 674 mL

Temperature (T) = 28°C

Pressure (P) = 741 mmHg.

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

Step 2:

Convert to the appropriate units.

For Volume:

1000mL = 1L

So, 674mL = 674/1000 = 0.674L

For Temperature:

Temperature in Kelvin = Temperature in Celsius + 273

Temperature in Celsius = 28°C

Temperature in Kelvin = 28°C + 273 = 301K

For Pressure:

760mmHg = 1atm

So, 741 mmHg = 741/760 = 0.975atm

Step 3:

Calculate the moles of the alkane.

The moles of the alkane can be found using the ideal gas equation, presented below:

Volume (V) = 0.674L

Temperature (T) = 301K

Pressure (P) = 0.975atm

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

Number of moles (n) =?

PV = nRT

n = PV /RT

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

n = 0.0266 moles

Step 4:

Calculate the alkane’s molar mass.

Mass of alkane = 1.17g

Number of moles = 0.0266moles

Molar Mass =?

Number of moles = Mass/Molar Mass

Molar Mass = Mass/Number of moles

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

Step 5:

Determine the molecular formula of the alkane.

This is based on:

The general formula for alkanes is CnH2n+2

To find the molecular formula, we start with n = 1, 2, 3, etc., until we find the 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

It can be observed that for n equal to 3, the molar mass is 44g/mol.

Thus, the molecular formula of the alkane is C3H8.

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