Concept explainers
(a)
Interpretation:
The bulb with higher pressure needs to be determined.
Concept introduction:
According to the
When at two different conditions gases are placed, then to determine the changed variable combined gas law is used. Below is the formula of combined gas law:
Here
- P1 and P2 are the pressure of gases
- V1 and V2 and volume of gases
- n1 and n2 number of moles
- T1 and T2 are the temperature of gases
Gas density is known as the ratio of mass of the gas and the volume occupied by that gas. The formula is as below:
Here, MM is the molar mass of the gas, V is the volume of gas, P is pressure of gas, T is temperature and R is the universal gas constant.
The kinetic model of gases is accounted for ideal gas behavior. The formula of average translational energy of gas is as below:
Here,
Et = average translational energy of gas
T = temperature in Kelvin
R = Universal gas constant
NA =
Effusion is known as the leakage of gas molecules from high to low pressure region via a pinhole. For any two gas molecules the formula to determine the time needed for effusion is as below:
Here u1 and u2 is the rate of effusion for gas1 and gas 2. MM1 and MM2 is the molar mass for gas1 and gas 2.
The whole pressure (Ptot ) exerted by the combination of gases equal to the addition of the partial pressure exerted through each gas.
As per the Dalton law of partial pressure mole fraction is the mole of each component present in total moles of compound:
Here, n1 is the mole of component, ntot is total moles and n1 /ntot mole fraction of gas 1.
Answer to Problem 80QAP
Pressure in both the bulbs will be same.
Explanation of Solution
The gas present in bulb A is N2 and bulb is NH3 . The moles of N2 and NH3 is 1 mol each. In both bulbs, the volume is same, and temperature is also same. The ideal gas equation is used to determine the ratio of pressure in bulb A (PA ) and bulb B (PB ) as below:
The ratio of both the gases are same which means nA and nB and same. Putting these values in the above equation:
Thus, the pressure in both the bulbs would be same.
(b)
Interpretation:
The bulb containing the gas with higher density needs to be determined.
Concept introduction:
According to the ideal
When at two different conditions gases are placed, then to determine the changed variable combined gas law is used. Below is the formula of combined gas law:
Here
- P1 and P2 are the pressure of gases
- V1 and V2 and volume of gases
- n1 and n2 number of moles
- T1 and T2 are the temperature of gases
Gas density is known as the ratio of mass of the gas and the volume occupied by that gas. The formula is as below:
Here, MM is the molar mass of the gas, V is the volume of gas, P is pressure of gas, T is temperature and R is the universal gas constant.
The kinetic model of gases is accounted for ideal gas behavior. The formula of average translational energy of gas is as below:
Here,
Et = average translational energy of gas
T = temperature in Kelvin
R = Universal gas constant
NA = Avogadro number
Effusion is known as the leakage of gas molecules from high to low pressure region via a pinhole. For any two gas molecules the formula to determine the time needed for effusion is as below:
Here u1 and u2 is the rate of effusion for gas1 and gas 2. MM1 and MM2 is the molar mass for gas1 and gas 2.
The whole pressure (Ptot ) exerted by the combination of gases equal to the addition of the partial pressure exerted through each gas.
As per the Dalton law of partial pressure mole fraction is the mole of each component present in total moles of compound:
Here, n1 is the mole of component, ntot is total moles and n1 /ntot mole fraction of gas 1.
Answer to Problem 80QAP
Bulb A has the higher density.
Explanation of Solution
The gas density is directly proportional to the molar mass of the gas. The molar mass of N2 is 28 g/ml and NH3 is 17 g/mol. The molar mass of N2 is higher than NH3 . Thus, the density of N2 would be higher.
So, the bulb A having the higher density.
(c)
Interpretation:
The bulb containing the molecule having higher kinetic energy needs to be determined.
Concept introduction:
According to the ideal gas law volume i.e. V, pressure i.e. P, number of moles i.e. m, temperature i.e. t and universal gas constant i.e. R is interrelated as below:
When at two different conditions gases are placed, then to determine the changed variable combined gas law is used. Below is the formula of combined gas law:
Here
- P1 and P2 are the pressure of gases
- V1 and V2 and volume of gases
- n1 and n2 number of moles
- T1 and T2 are the temperature of gases
Gas density is known as the ratio of mass of the gas and the volume occupied by that gas. The formula is as below:
Here, MM is the molar mass of the gas, V is the volume of gas, P is pressure of gas, T is temperature and R is the universal gas constant.
The kinetic model of gases is accounted for ideal gas behavior. The formula of average translational energy of gas is as below:
Here,
Et = average translational energy of gas
T = temperature in Kelvin
R = Universal gas constant
NA = Avogadro number
Effusion is known as the leakage of gas molecules from high to low pressure region via a pinhole. For any two gas molecules the formula to determine the time needed for effusion is as below:
Here u1 and u2 is the rate of effusion for gas1 and gas 2. MM1 and MM2 is the molar mass for gas1 and gas 2.
The whole pressure (Ptot ) exerted by the combination of gases equal to the addition of the partial pressure exerted through each gas.
As per the Dalton law of partial pressure mole fraction is the mole of each component present in total moles of compound:
Here, n1 is the mole of component, ntot is total moles and n1 /ntot mole fraction of gas 1.
Answer to Problem 80QAP
For both the bulbs kinetic energy is same.
Explanation of Solution
The average kinetic energy formula displays that average kinetic energy is directly proportional to the kinetic temperature. The temperatures in both the bulbs are same. Thus, the kinetic energy in bulb A and bulb B would be same.
(d)
Interpretation:
The bulb containing the gas that moves with the faster molecular speed needs to be determined.
Concept introduction:
According to the ideal gas law volume i.e. V, pressure i.e. P, number of moles i.e. m, temperature i.e. t and universal gas constant i.e. R is interrelated as below:
When at two different conditions gases are placed, then to determine the changed variable combined gas law is used. Below is the formula of combined gas law:
Here
- P1 and P2 are the pressure of gases
- V1 and V2 and volume of gases
- n1 and n2 number of moles
- T1 and T2 are the temperature of gases
Gas density is known as the ratio of mass of the gas and the volume occupied by that gas. The formula is as below:
Here, MM is the molar mass of the gas, V is the volume of gas, P is pressure of gas, T is temperature and R is the universal gas constant.
The kinetic model of gases is accounted for ideal gas behavior. The formula of average translational energy of gas is as below:
Here,
Et = average translational energy of gas
T = temperature in Kelvin
R = Universal gas constant
NA = Avogadro number
Effusion is known as the leakage of gas molecules from high to low pressure region via a pinhole. For any two gas molecules the formula to determine the time needed for effusion is as below:
Here u1 and u2 is the rate of effusion for gas1 and gas 2. MM1 and MM2 is the molar mass for gas1 and gas 2.
The whole pressure (Ptot ) exerted by the combination of gases equal to the addition of the partial pressure exerted through each gas.
As per the Dalton law of partial pressure mole fraction is the mole of each component present in total moles of compound:
Here, n1 is the mole of component, ntot is total moles and n1 /ntot mole fraction of gas 1.
Answer to Problem 80QAP
NH3 having the higher average speed.
Explanation of Solution
As per the effusion formula shows the average effusion speed of a gas is inversely proportional to the square root of the molar mass of the gas. This means the gas with higher molar mass will have slower average speed for the effusion. The molar mass of N2 is higher than NH3 . Thus, the gas having the higher average speed would be NH3.
(e)
Interpretation:
The change in pressure when valve between the two bulbs is opened needs to be calculated.
Concept introduction:
According to the ideal gas law volume i.e. V, pressure i.e. P, number of moles i.e. m, temperature i.e. t and universal gas constant i.e. R are interrelated as below:
When at two different conditions gases are placed, then to determine the changed variable combined gas law is used. Below is the formula of combined gas law:
Here
- P1 and P2 are the pressure of gases.
- V1 and V2 and volume of gases.
- n1 and n2 number of moles.
- T1 and T2 temperature of gases.
Gas density is known as the ratio of mass of the gas and the volume occupied by that gas. The formula is as below:
Here, MM is the molar mass of the gas, V is the volume of gas, P is pressure of gas, T is temperature and R is the universal gas constant.
The kinetic model of gases is accounted for ideal gas behavior. The formula of average translational energy of gas is as below:
Here,
Et = average translational energy of gas
T = temperature in Kelvin
R = Universal gas constant
NA = Avogadro number
Effusion is known as the leakage of gas molecules from high to low pressure region via a pinhole. For any two gas molecules the formula to determine the time needed for effusion is as below:
Here u1 and u2 is the rate of effusion for gas1 and gas 2. MM1 and MM2 is the molar mass for gas1 and gas 2.
The whole pressure (Ptot ) exerted by the combination of gases equal to the addition of the partial pressure exerted through each gas.
As per the Dalton law of partial pressure mole fraction is the mole of each component present in total moles of compound:
Here, n1 is the mole of component, ntot is total moles and n1 /ntot mole fraction of gas 1.
Answer to Problem 80QAP
Pressure in both the bulbs will be same.
Explanation of Solution
The open valve will maintain equilibrium amid gases in each bulb. Because all the conditions like number of moles, volume and temperature are same. Thus, the pressure would be same.
(f)
Interpretation:
The fraction of the total pressure due to He gas needs to be determined.
Concept introduction:
According to the ideal gas law volume i.e. V, pressure i.e. P, number of moles i.e. m, temperature i.e. t and universal gas constant i.e. R are interrelated as below:
When at two different conditions gases are placed, then to determine the changed variable combined gas law is used. Below is the formula of combined gas law:
Here
- P1 and P2 are the pressure of gases
- V1 and V2 and volume of gases
- n1 and n2 number of moles
- T1 and T2 are the temperature of gases
Gas density is known as the ratio of mass of the gas and the volume occupied by that gas. The formula is as below:
Here, MM is the molar mass of the gas, V is the volume of gas, P is pressure of gas, T is temperature and R is the universal gas constant.
The kinetic model of gases is accounted for ideal gas behavior. The formula of average translational energy of gas is as below:
Here,
Et = average translational energy of gas
T = temperature in Kelvin
R = Universal gas constant
NA = Avogadro number
Effusion is known as the leakage of gas molecules from high to low pressure region via a pinhole. For any two gas molecules the formula to determine the time needed for effusion is as below:
Here u1 and u2 is the rate of effusion for gas1 and gas 2. MM1 and MM2 is the molar mass for gas1 and gas 2.
The whole pressure (Ptot ) exerted by the combination of gases equal to the addition of the partial pressure exerted through each gas.
As per the Dalton law of partial pressure mole fraction is the mole of each component present in total moles of compound:
Here, n1 is the mole of component, ntot is total moles and n1 /ntot mole fraction of gas 1.
Answer to Problem 80QAP
The fraction of helium of the total pressure would be ½.
Explanation of Solution
The moles of He added in the system is 2 mol. The moles of N2 is 1 mol and NH3 is 1 mol. The total mole number of gases in the system is calculated as below:
Thus, the total number of moles is 4 mol.
The values of ntot and nHe is substituted in equation of Dalton’s law of partial pressure shown below:
Thus, the fraction of helium to the total pressure would be
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Chapter 5 Solutions
Student Solutions Manual For Masterton/hurley's Chemistry: Principles And Reactions, 8th
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