Use the following information to identify element \(\mathrm{A}\) and compound \(\mathrm{B}\), then answer questions a and \(\mathrm{b}\). An empty glass container has a mass of \(658.572 \mathrm{~g} .\) It has a mass of \(659.452 \mathrm{~g}\) after it has been filled with nitrogen gas at a pressure of 790 . torr and a temperature of \(15^{\circ} \mathrm{C}\). When the container is evacuated and refilled with a certain element (A) at a pressure of 745 torr and a temperature of \(26^{\circ} \mathrm{C}\), it has a mass of \(660.59 \mathrm{~g}\) Compound \(\mathrm{B}\), a gaseous organic compound that consists of \(85.6 \%\) carbon and \(14.4 \%\) hydrogen by mass, is placed in a stainless steel vessel \((10.68 \mathrm{~L})\) with excess oxygen gas. The vessel is placed in a constant-temperature bath at \(22^{\circ} \mathrm{C}\). The pressure in the vessel is \(11.98 \mathrm{~atm}\). In the bottom of the vessel is a container that is packed with Ascarite and a desiccant. Ascarite is asbestos impregnated with sodium hydroxide; it quantitatively absorbs carbon dioxide: $$ 2 \mathrm{NaOH}(s)+\mathrm{CO}_{2}(g) \longrightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l) $$ The desiccant is anhydrous magnesium perchlorate, which quantitatively absorbs the water produced by the combustion reaction as well as the water produced by the above reaction. Neither the Ascarite nor the desiccant reacts with compound \(\mathrm{B}\) or oxygen. The total mass of the container with the Ascarite and desiccant is \(765.3 \mathrm{~g}\) The combustion reaction of compound \(\mathrm{B}\) is initiated by a spark. The pressure immediately rises, then begins to decrease, and finally reaches a steady value of \(6.02 \mathrm{~atm} .\) The stainless steel vessel is carefully opened, and the mass of the container inside the vessel is found to be \(846.7 \mathrm{~g}\). \(\mathrm{A}\) and \(\mathrm{B}\) react quantitatively in a \(1: 1\) mole ratio to form one mole of the single product, gas \(\mathrm{C}\). a. How many grams of \(\mathrm{C}\) will be produced if \(10.0 \mathrm{~L} \mathrm{~A}\) and \(8.60 \mathrm{~L}\) \(\mathrm{B}\) (each at STP) are reacted by opening a stopcock connecting the two samples? b. What will be the total pressure in the system?

Step by step solution

01

Determine the moles of nitrogen gas in the container

First, let's calculate the number of moles of nitrogen gas present in the container using the Ideal Gas Law: \(PV = nRT\), where \(P\) is the pressure, \(V\) is the volume, \(n\) is the number of moles, \(R\) is the Ideal Gas Constant and \(T\) is the temperature in Kelvin scale. To calculate the moles, rearrange the formula: \(n = \frac{PV}{RT}\) Given, \[\] Mass of empty container = 658.572 g \[\] Mass of the container filled with nitrogen = 659.452 g \[\] Pressure of nitrogen, P = 790 torr = 790 / 760 atm (1 atm = 760 torr) \[\] Temperature = 15°C = 15 + 273.15 K = 288.15 K So, \(V = \frac{Mass\, of\, nitrogen}{Density\, of\, nitrogen}\) Density of nitrogen (\(\rho_N\)) at STP = 1.250 g/L \[\] Mass of nitrogen = (mass of the container filled with nitrogen) - (mass of the empty container) = 0.88 g \[ \] Now, \(V = \frac{0.88}{1.250} = 0.704 L\) Let's plug the values in the rearranged formula for calculating 'n': \(n_N = \frac{(790/760)(0.704)}{0.0821(288.15)}\)

02

Calculate the molar mass of nitrogen

Molar mass (M) can be calculated using the formula: M = \(\frac{mass\,of\,nitrogen\, gas}{moles\,of\,nitrogen\, gas}\) Now, plug the values to calculate molar mass of nitrogen: \(M_N = \frac{0.88}{n_N}\)

03

Identify Element A

Now, calculate the moles of element A using the Ideal gas law, given pressure is 745 torr and temperature is 26°C. \[ \] Temperature of element A = 26°C = 26 + 273.15 K = 299.15 K \[ \] Pressure of element A = 745 torr = 745 / 760 atm \[ \] Mass of element A = (mass of container filled with element A) - (mass of empty container) = 660.59 - 658.572 = 2.018 g Now, let's calculate the moles of element A as follows: \(n_A = \frac{(745/760)(0.704)}{0.0821(299.15)}\) Molar mass of element A = \(\frac{mass\,of\,element\,A}{moles\,of\,element\,A}\) Compare the molar mass of element A with the periodic table to identify the element.

04

Identify Compound B

Let the empirical formula of compound B be CxHy. Given that it contains 85.6% carbon and 14.4% hydrogen by mass. \[ \] Carbon: \(\frac{85.6}{12.01}\) (molar mass of C is 12.01) \[ \] Hydrogen: \(\frac{14.4}{1.008}\) (molar mass of H is 1.008) Since combustion of B is CxHy + O2 -> xCO2 + (y/2)H2O Use the above information and the mass of the container in the vessel to determine the empirical formula of compound B.

05

Calculate the quantity of Compound C produced (Question: a)

It is given that A and B react quantitatively in a 1:1 mole ratio to form one mole of C. \[ \] Amount of A = 10.0 L \[ \] Amount of B = 8.60 L Since they react in a 1:1 ratio, Amount of C produced = min(10.0 L, 8.60 L) = 8.60 L Now, use the molar mass of A and B to calculate the grams of C that will be produced.

06

Calculate the total pressure in the system (Question: b)

Total pressure can be calculated using the mole fraction and individual partial pressures of A and B. Total pressure (P_total) = Partial pressure of A (P_A) + Partial pressure of B (P_B) Use the given amounts of A and B and their respective molar masses to calculate the total pressure in the system.

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