An herbicide is found to contain only \(\mathrm{C}, \mathrm{H}, \mathrm{N},\) and \(\mathrm{Cl} .\) The complete combustion of a 100.0 -mg sample of the herbicide in excess oxygen produces \(83.16 \mathrm{~mL}\) of \(\mathrm{CO}_{2}\) and \(73.30 \mathrm{~mL}\) of \(\mathrm{H}_{2} \mathrm{O}\) vapor expressed at STP. A separate analysis shows that the sample also contains $16.44 \mathrm{mg}\( of \)\mathrm{Cl}$. (a) Determine the percentage of the composition of the substance. (b) Calculate its empirical formula. (c) What other information would you need to know about this compound to calculate its true molecular formula?

Short Answer

Expert verified
(a) The percentage composition of the herbicide is calculated as follows: - C: Percentage = \(\frac{mass\;of\;C}{total\;mass\;of\;sample}\) * 100 - H: Percentage = \(\frac{mass\;of\;H}{total\;mass\;of\;sample}\) * 100 - N: Percentage = \(\frac{mass\;of\;N}{total\;mass\;of\;sample}\) * 100 - Cl: Percentage = \(\frac{mass\;of\;Cl}{total\;mass\;of\;sample}\) * 100 (b) The empirical formula is found by dividing the moles of each element by the smallest number of moles observed and rounding to the nearest whole number, resulting in CxHyNzClw. (c) To determine the true molecular formula, additional information is needed, such as the molar mass of the compound or structural information like spectroscopy data or a description of its structure. This would help us find the actual molecular formula by comparing it to the empirical formula.

Step by step solution

01

Calculate moles of C and H from combustion volumes.

Remember that STP conditions are 0°C (273.15 K) and 1 atm pressure. We can use the ideal gas law to calculate the moles of CO2 and H2O formed. The ideal gas law is given by: PV = nRT Where P is pressure, V is volume, n is the number of moles, R is the gas constant (0.0821 L*(atm)/(mol*K) for STP), and T is the temperature. Given the volumes of CO2 and H2O, we can calculate the moles of each compound and then determine the moles of carbon and hydrogen. For CO2: (1 atm) * \(83.16 \times 10^{-3} L = n \times 0.0821\frac{L.atm}{mol. K}\) * (273.15 K) For H2O: (1 atm) * \(73.30 \times 10^{-3} L = n \times 0.0821\frac{L.atm}{mol. K}\) * (273.15 K)
02

Find moles of Cl and calculate moles of N.

We are given the mass of Cl in the sample, i.e., 16.44 mg. To find the moles of Cl, we can use the molar mass of Cl (35.45 g/mol). Moles of Cl = \(\frac{16.44 \times 10^{-3} g }{35.45 g/mol}\). Next, since the sample contains only C, H, N and Cl, we can subtract the masses of C, H and Cl from the sample's total mass to find the mass of N. We can then use the molar mass of N (14.01 g/mol) to find the moles of N in the sample.
03

Determine the percentage composition.

We can now calculate the percentage of each element in the sample by dividing the mass of the element by the total mass of the sample, and then multiplying it by 100. Percentage composition = \(\frac{mass\;of\;element}{total\;mass\;of\;sample}\) * 100 Calculate the percentage for C, H, N, and Cl.
04

Calculate the empirical formula.

To find the empirical formula, divide the moles of each element by the smallest number of moles observed. C: moles of C / smallest number of moles H: moles of H / smallest number of moles N: moles of N / smallest number of moles Cl: moles of Cl / smallest number of moles Round each calculated value to the nearest whole number to find the empirical formula (CxHyNzClw).
05

Discuss the information needed for the true molecular formula.

To find the true molecular formula of the compound, we need additional information, such as the molar mass of the compound or some other structural information, like spectroscopy data or a description of its structure. This information would help us to determine the actual molecular formula by comparing it to the empirical formula obtained in Step 4. The true molecular formula is a multiple of the empirical formula.

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Most popular questions from this chapter

A \(4.00-\mathrm{g}\) sample of a mixture of \(\mathrm{CaO}\) and \(\mathrm{BaO}\) is placed in a 1.00-L vessel containing \(\mathrm{CO}_{2}\) gas at a pressure of \(97.33 \mathrm{kPa}\) and a temperature of \(25^{\circ} \mathrm{C}\). The \(\mathrm{CO}_{2}\) reacts with the \(\mathrm{CaO}\) and \(\mathrm{BaO},\) forming \(\mathrm{CaCO}_{3}\) and \(\mathrm{BaCO}_{3}\). When the reaction is complete, the pressure of the remaining \(\mathrm{CO}_{2}\) is \(20.0 \mathrm{kPa}\). (a) Calculate the number of moles of \(\mathrm{CO}_{2}\) that have reacted. (b) Calculate the mass percentage of \(\mathrm{CaO}\) in the mixture.

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Determine whether each of the following changes will increase, decrease, or not affect the rate with which gas molecules collide with the walls of their container: (a) increasing the volume of the container, \((\mathbf{b})\) increasing the temperature, (c) increasing the molar mass of the gas.

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