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Interpretation: The total pressure of given reaction tank and the partial pressures of nitrogen gas at 127oC in the given reaction tank of 250 L are needed to be determined if the mass of dimethyl hydrazine is 150 g.
Concept introduction:
- Number of moles of a substance,
From its given mass is,
Number of moles = Given massMolecular mass
- Mole ratios between the reactant and products of a reaction are depends upon the coefficients of respective reactant in a balanced chemical equation.
- Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.
Pressure of the gas, according to ideal gas equation,
Pressure = Number of moles × R × TemperatureVolume
- Total pressure of a tank containing mixture of gases is the sum of individual partial pressures of constituted gases.
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Answer to Problem 107E
Answer
The partial pressure of N2 in the given reaction is 0.98 atm.
Total pressure of given reaction container is 2.93 atm.
Explanation of Solution
Explanation
- To find: the number of moles of dimethyl hydrazine from its given mass.
The number of moles of dimethyl hydrazine is 2.5 mol.
The given mass for dimethyl hydrazine is 150 g.
Number of moles of a substance from its given mass is,
Number of moles = Given massMolecular mass
Therefore, the number of moles of dimethyl hydrazine in the flask is,
Number of moles of dimethyl hydrazine = 150 g60.1 g/mol = 2.5 mol
- To find: the molar ratio between produced N2, H2O and CO2 with the reactant dimethyl hydrazine and the number of moles of each produced gases in the given reaction
3 moles of N2 is produced by 1 mole of dimethyl hydrazine in the given reaction.
4 moles of H2O is produced by 1 mole of dimethyl hydrazine in the given reaction.
2 moles of CO2 is produced by 1 mole of dimethyl hydrazine in the given reaction.
The number of moles of produced N2 is 7.5 mol.
The number of moles of produced H2O is 10 mol.
The number of moles of produced CO2 is 5 mol.
For N2,
- The balanced equation of the reaction is given as
(CH3)2N2H2 + 2 N2O4 → 3 N2 + 4 H2O + 2 CO2 .
Here the 1 moles of dimethyl hydrazine is producing 3 moles of N2.
That is,
The mole ratio between dimethyl hydrazine and N2 is,
1:3
- The number of moles of reacted dimethyl hydrazine is 2.5 mol.
The mole ratio between dimethyl hydrazine and produced N2 is 1:3.
Therefore,
The number of moles of produced N2 is,
2.5 mol × 3 mol N2 1 mol dimethyl hydrazine = 7.5 mol
Hence, the number of moles of produced N2 is 7.5 mol.
For H2O,
- The balanced equation of the reaction is given as
(CH3)2N2H2 + 2 N2O4 → 3 N2 + 4 H2O + 2 CO2 .
Here the 1 moles of dimethyl hydrazine is producing 4 moles of H2O.
That is,
The mole ratio between dimethyl hydrazine and H2O is,
1:4
- The number of moles of reacted dimethyl hydrazine is 2.5 mol.
The mole ratio between dimethyl hydrazine and produced H2O is 1:3.
Therefore,
The number of moles of produced H2O is,
2.5 mol × 4 mol H2O 1 mol dimethyl hydrazine = 10 mol
Hence, the number of moles of produced H2O is 10 mol.
For CO2,
- The balanced equation of the reaction is given as
(CH3)2N2H2 + 2 N2O4 → 3 N2 + 4 H2O + 2 CO2 .
Here the 1 moles of dimethyl hydrazine is producing 2 moles of CO2.
That is,
The mole ratio between dimethyl hydrazine and CO2 is,
1:2
- The number of moles of reacted dimethyl hydrazine is 2.5 mol.
The mole ratio between dimethyl hydrazine and produced CO2 is 1:2.
Therefore,
The number of moles of produced CO2 is,
2.5 mol × 2 mol CO2 1 mol dimethyl hydrazine = 5 mol
Hence, the number of moles of produced N2 is 5 mol.
- To find: the partial pressures nitrogen gas in the given reaction.
The partial pressure of N2 in the given reaction is 0.98 atm.
The number of moles of produced N2 is calculated as 7.5 mol.
The temperature of reaction is given as 127oC = (127 + 273 )K = 400 K
The volume of tank is given as 250 L.
Pressure of a gas, according to ideal gas equation,
Pressure = Number of moles × R × TemperatureVolume
Therefore,
The partial pressure of N2 in the given reaction is,
PN2 = 7.5 mol × 0.08206 L atm / K mol × 400 K250 L = 0.98 atm
Hence,
The partial pressure of N2 in the given reaction is 0.98 atm.
- To find: the partial pressures of H2O in the given reaction.
The partial pressure of H2O in the given reaction is 1.3 atm.
The number of moles of produced H2O is calculated as 10 mol.
The temperature of reaction is given as 127oC = (127 + 273 )K = 400 K
The volume of tank is given as 250 L.
Pressure of a gas, according to ideal gas equation,
Pressure = Number of moles × R × TemperatureVolume
Therefore,
The partial pressure of H2O in the given reaction is,
PH2O = 10 mol × 0.08206 L atm / K mol × 400 K250 L = 1.3 atm
Hence,
The partial pressure of H2O in the given reaction is 1.3 atm.
- To find: the partial pressures of CO2 in the given reaction.
The partial pressure of CO2 in the given reaction is 0.65 atm.
The number of moles of produced CO2 is calculated as 5 mol.
The temperature of reaction is given as 127oC = (127 + 273 )K = 400 K
The volume of tank is given as 250 L.
Pressure of a gas, according to ideal gas equation,
Pressure = Number of moles × R × TemperatureVolume
Therefore,
The partial pressure of CO2 in the given reaction is,
PCO2 = 5 mol × 0.08206 L atm / K mol × 400 K250 L = 0.65 atm
Hence,
The partial pressure of CO2 in the given reaction is 0.65 atm.
- To find: the total pressure of the given reaction tank.
The total pressure of the given reaction tank is 2.93 atm.
The total pressure of a tank containing mixture of gases is the sum of individual partial pressures of constituted gases.
The partial pressures of products in given reaction are calculated above.
Therefore,
The total pressure of the given reaction tank is
PN2 + PH2O + PCO2 = 0.98 atm + 1.3 atm + 0.65 atm = 2.93 atm
Hence, the final total pressure of the given reaction tank is 2.93 atm.
Conclusion
The partial pressures of N2, H2O and CO2 gases in the given reaction is determined by using ideal gas equation. The total pressure of container is determined by adding the partial pressures of N2 H2O and CO2 gases.
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