Answer:
The empirical formula is C4H8O
The molecular formula is C8H16O2
Step-by-step explanation:
Step 1: Data given
Mass of the unknown sample = 5.90 grams
Temperature = 20.0 °C
PRessure = 1 bar
Volume CO2 = 7.98 L
Volume of H2O = 5.91 mL = 0.00591 L
Density of water at 20.0 °C = 0.998 g/mL
Step 2: Calculate moles CO2
p*V= n*R*T
⇒ with p = the pressure = 1 bar = 0.986923 atm
⇒ with V = the volume of CO2 = 7.98 L
⇒ with n = the number of moles CO2 = TO BE DETERMINED
⇒ with R = The gas constant = 0.08206 L*atm/K*mol
⇒ with T = the temperature = 20.0 °C = 293 Kelvin
n = (p*V)/(R*T)
n = (0.986923*7.98)/(0.08206*293)
n = 0.3276 moles
Step 3: Calculate mass water
Mass water = volume * density
Mass water = 5.91 mL * 0.998 g/mL
Mass water = 5.89818 grams
Step 4: Calculate moles H2O
Moles H2O = 5.89818 grams / 18.02 g/mol
Moles H2O = 0.3273 moles
Step 5: Calculate moles of hydrogen
For 1 mol H2O we have 2 moles of hydrogen
For 0.3273 moles H2O we have 2*0.3273 moles = 0.6546 moles
Step 6: Calculate moles of carbon
1 mol CO2 has 1 mol C
0.3276 moles moles CO2 has 0.3276 moles C
Step 7: Calculate mass C
Mass C = 0.3276 moles * 12.0 g/mol
Mass C = 3.93 grams
Step 8: calculate mass of oxygen
Mass of O = mass of sample - (mass of C + mass of H)
Mass O = 5.90 grams - (3.93 +0.661 )
Mass O = 1.309 grams
Step 9: Calculate moles O
Moles O = 1.309 grams / 16.0 g/mol
Moles O = 0.0818 moles
Step 10: Calculate mol ratio
We divide by the smallest amount of moles
C: 0.3276 / 0.0818 = 4
H: 0.6546 / 0.0818 = 8
O: 0.0818 / 0.0818 = 1
The empirical formula is C4H8O
If the molar mass is 144.2
The molecular formula is C8H16O2