A compound containing only C, H, and N yields the following data.
(i) Complete combustion of 34.8 mg of the compound produced 33.3 mg of CO2 and 40.9 mg of H2O.
(ii) A 66.3-mg sample of the compound was analyzed for nitrogen by the Dumas method, giving 36.2 mL of N2 at 740. torr and 25°C
(iii) The effusion rate of the compound as a gas was measured and found to be 24.6 mL/min. The effusion rate of argon gas, under identical conditions, is 26.4 mL/min.
What is the molecular formula of the compound?
somehow I got it right with CH6N2. Thanks
To determine the molecular formula of the compound, we need to analyze the given data and calculate the empirical formula first. The empirical formula represents the simplest whole-number ratio of atoms present in a compound.
Let's start by calculating the number of moles of CO2 and H2O produced in the combustion reaction:
1. Moles of CO2:
- Mass of CO2 produced = 33.3 mg = 0.0333 g
- Molar mass of CO2 = 44.01 g/mol
- Moles of CO2 = (mass of CO2 produced) / (molar mass of CO2) = 0.0333 g / 44.01 g/mol
2. Moles of H2O:
- Mass of H2O produced = 40.9 mg = 0.0409 g
- Molar mass of H2O = 18.02 g/mol
- Moles of H2O = (mass of H2O produced) / (molar mass of H2O) = 0.0409 g / 18.02 g/mol
Next, we need to determine the ratio of carbon (C) to hydrogen (H) atoms in the compound. We can do this by comparing the moles of CO2 and H2O produced.
3. Moles of C:
- From the balanced combustion reaction, we know that 1 mole of CO2 contains 1 mole of carbon. Therefore, the number of moles of C in the compound is equal to the moles of CO2.
4. Moles of H:
- From the balanced combustion reaction, we know that 1 mole of H2O contains 2 moles of hydrogen. Therefore, the number of moles of H in the compound is equal to 2 times the moles of H2O.
Now, let's calculate the number of moles of nitrogen (N) using the ideal gas law and the Dumas method data:
5. Volume of N2:
- Volume of N2 = 36.2 mL = 0.0362 L
- Temperature = 25°C = 25 + 273 = 298 K
- Pressure = 740 torr = 740 mmHg
(Assuming the gas behaves ideally)
- Moles of N2 = (volume of N2) * (pressure) / (R * temperature), where R is the ideal gas constant (0.0821 L·atm/(mol·K))
Finally, we can find the empirical formula by evaluating the ratios between the number of moles of each element:
6. Determine the empirical formula:
- Divide the moles of each element by the smallest number of moles obtained.
- Round the obtained ratio to the nearest whole number.
Now, using the empirical formula, we can find the molecular formula if we have additional information about the molar mass of the compound or by comparing it to known compounds. However, without additional information, we cannot determine the exact molecular formula from the given data alone.