30 cubic-centimetre hydrocarbon requires 90 cubic-centimetre of oxygen for complete combustion and 60 cubic-centimetre of carbondioxide is formed .What is the formula of hydrocarbon?
To find the formula of the hydrocarbon, we need to analyze the balanced chemical equation for the combustion reaction.
Let's start by writing the balanced equation for the combustion of the hydrocarbon:
Hydrocarbon + Oxygen → Carbon Dioxide + Water
Now let's determine how many moles of each substance are involved in the reaction.
We know that 30 cubic centimeters of the hydrocarbon requires 90 cubic centimeters of oxygen, and 60 cubic centimeters of carbon dioxide are produced.
First, we convert the volumes to moles, using the ideal gas law:
PV = nRT
Where:
P = pressure (assumed constant)
V = volume
n = number of moles
R = ideal gas constant
T = temperature (assumed constant)
Since the pressure, temperature, and volume are constant, we can simplify the equation to:
n = (V × P) / RT
Assuming standard temperature and pressure (STP), which is 1 atmosphere and 273.15 Kelvin, the equation becomes:
n = (V × P) / (0.0821 × 273.15)
For the hydrocarbon:
n(hydrocarbon) = (30 cc × 1 atm) / (0.0821 × 273.15)
Now, we find the number of moles of oxygen required for combustion. We can use the stoichiometry of the balanced equation to determine the ratio between the hydrocarbon and oxygen:
hyd : O₂ → 1 : 3
n(hydrocarbon) × 3 = n(oxygen)
n(oxygen) = (n(hydrocarbon) × 3) = ((30 cc × 1 atm) / (0.0821 × 273.15)) × 3
Finally, using the stoichiometry of the balanced equation, we can determine the number of moles of carbon dioxide produced:
hyd : O₂ → CO₂ : H₂O
1 : 3 → 60 cc
Using the same ratio:
n(hydrocarbon) × 1 = n(CO₂) × (60 cc / 3)
n(CO₂) = (n(hydrocarbon) × 1) / (60 cc / 3) = ((30 cc × 1 atm) / (0.0821 × 273.15)) / (60 cc / 3)
Now that we have the number of moles of each substance, we can find their molar masses and determine the empirical formula of the hydrocarbon.
The molar mass of carbon dioxide (CO₂) is 44 g/mol, which means 1 mole of CO₂ weighs 44 grams.
The molar mass of the hydrocarbon can be calculated by dividing the mass of the hydrocarbon by the number of moles:
m(hydrocarbon) = ((30 cc × 1 atm) / (0.0821 × 273.15)) × molar mass(hydrocarbon)
The molar mass of carbon dioxide produced can be calculated by dividing the mass of carbon dioxide by the number of moles:
m(CO₂) = ((30 cc × 1 atm) / (0.0821 × 273.15)) / (60 cc / 3) × molar mass(CO₂)
Once we have the molar masses of the hydrocarbon and carbon dioxide, we can simply compare the two to determine the empirical formula of the hydrocarbon.
To find the empirical formula, we divide the molar mass of the hydrocarbon by the molar mass of carbon dioxide and round to the nearest whole number, as they should be in a simple ratio.
Empirical formula = molar mass(hydrocarbon) / molar mass(CO₂)
This will give us the simplest whole-number ratio of the atoms in the hydrocarbon, allowing us to determine its empirical formula.
So, by following these steps and calculating the values, we can find the empirical formula of the hydrocarbon.