An empty glass container has a mass of 418.634 grams. It has a mass of 419.514 grams after it has been filled with nitrogen gas at a pressure of 790 mmHg and a temperature of 15oC. When the container is evacuated and refilled with a certain element X at a pressure of 745 mmHg and a temperature of 26oC, it has a mass of 420.652 grams.
Compound Y, a gaseous organic compound that consists of 88.9% carbon and 11.1 % hydrogen by mass, is placed in a stainless steel vessel ( 10.68 L) with excess oxygen gas. The vessel is placed in a constant temperature bath at 22oC. The pressure in the vessel is 9.970 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 reacts with and quantitatively absorbs carbon dioxide:
2NaOH (s) + CO2 (g) → Na2CO3(s) + H2O(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 Y or oxygen. The total mass of the container with the Ascarite and the desiccant is 746.3 grams.
The combustion of compound Y is initiated by a spark. The pressure in the container immediately rises, then begins to decrease and finally reaches a steady value of 1.51 atm.The stainless vessel is carefully opened and the mass of the container inside the vessel is found to be 878.7 grams.
X and Y react quantitatively in a 2:1 mole ratio to form one mole of the single product, gas Z.
a) How many grams of Z will be produced if 11.0 L of X and 9.60 L of Y (each at STP) are reacted by opening a stopcock connecting the 2 sample containers?
b) What will be the total pressure in the system? Assume all reactants and products are gases. Temp = 0oC
I already figured out that element x is Cl2, and I think that element y is c4h6cl4 but I'm not sure, and also for the grams of the product I got 48.1199grams, but also not very sure. I don't really know how to find total pressure
To solve this problem, we need to use the ideal gas law equation: 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.
a) First, we need to find the number of moles of X and Y at STP (standard temperature and pressure).
For X:
Given volume = 11.0 L
Standard temperature = 0°C = 273.15 K
Using the ideal gas law:
PV = nRT
(745 mmHg)(11.0 L) = nX(0.0821 L.atm/mol.K)(273.15 K)
Converting mmHg to atm:
P(atm) = 745 mmHg / 760 mmHg/atm = 0.979 atm
Substituting the values:
(0.979 atm)(11.0 L) = nX(0.0821 L.atm/mol.K)(273.15 K)
nX = (0.979 atm * 11.0 L) / (0.0821 L.atm/mol.K * 273.15 K)
nX = 0.44 mol
For Y:
Given volume = 9.60 L
Using the ideal gas law:
PV = nRT
(9.970 atm)(10.68 L) = nY(0.0821 L.atm/mol.K)(295.15 K)
Substituting the values:
(9.970 atm)(10.68 L) = nY(0.0821 L.atm/mol.K)(295.15 K)
nY = (9.970 atm * 10.68 L) / (0.0821 L.atm/mol.K * 295.15 K)
nY = 3.71 mol
The reaction of X and Y occurs in a 2:1 mole ratio, so the limiting reactant is X with 0.44 mol. Therefore, only 0.44 mol of Z can be formed.
To find the mass of Z, we need to know the molar mass of Z.
b) The total pressure in the system is found by adding the partial pressures of X and Y gases.
Partial pressure is calculated using the ideal gas law:
PV = nRT
For X:
P(atm) = 745 mmHg / 760 mmHg/atm = 0.979 atm
For Y:
P(atm) = 9.970 atm
Total pressure:
P_total = P_X + P_Y
P_total = 0.979 atm + 9.970 atm = 10.949 atm
To solve this problem, we need to use the ideal gas law equation, 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.
a) To find the number of moles of X and Y, we need to use the ideal gas law equation. However, we don't have the volume of X and Y, so we need to calculate it.
For X:
1. Convert the pressure from mmHg to atm: 745 mmHg = 745/760 atm.
2. Convert the temperature from degrees Celsius to Kelvin: 26oC + 273.15 = 299.15 K.
3. Rearrange the ideal gas law equation to solve for V: V = (nRT) / P.
4. Calculate the volume of X: V = (nRT) / P = (420.652 g / molar mass of X) * (0.0821 L*atm/(mol*K)) * (299.15 K) / (745/760 atm).
For Y:
1. Convert the pressure from atm to mmHg: 9.970 atm = 9.970 * 760 mmHg.
2. Convert the temperature from degrees Celsius to Kelvin: 22oC + 273.15 = 295.15 K.
3. Rearrange the ideal gas law equation to solve for V: V = (nRT) / P.
4. Calculate the volume of Y: V = (nRT) / P = (10.68 L) - (746.3 g / molar mass of Y) * (0.0821 L*atm/(mol*K)) * (295.15 K) / (9.970 * 760 mmHg).
Once we have the volumes of X and Y, we can convert them to moles using the ideal gas law equation: n = PV / RT.
Since the ratio of X and Y in the reaction is 2:1, we can determine the number of moles of Z produced.
b) To find the total pressure in the system, we need to calculate the partial pressures of X, Y, and Z. Since the volume is given as 11.0 L for X and 9.60 L for Y at STP (Standard Temperature and Pressure, which is 0oC and 1 atm), we can assume that the partial pressures of X and Y are 1 atm each. Since the ratio of X and Y in the reaction is 2:1, the partial pressure of Z will be half of the partial pressure of X or Y.
In this case, the total pressure in the system will be the sum of the partial pressures of X, Y, and Z.
Please note that actual calculations to determine the molar masses and perform the conversions are required to obtain the exact answers.