(a)
Interpretation:
The tank containing higher mass 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 time1 and time2 is the time of effusion for gas1 and gas 2. MM1 and MM2 is the molar mass for gas1 and gas 2.
Answer to Problem 79QAP
The mass of SO2 in tank A is GT the mass of O2 in tank B.
Explanation of Solution
Below is the expression of ideal gas equation:
Here, 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
We have
Thus, no of moles is constant then molar mass is directly proportional to the mass of gases and if the molar mass is greater then mass of the gas will be greater as well.
So, let’s consider the number of moles in each tank to be one:
Thus, the mass of SO2 in tank A is GT the mass of O2 in tank B.
(b)
Interpretation:
The gas between CH4 and SO2 with higher average translational energy 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, time1 and time2 is the time of effusion for gas1 and gas 2. MM1 and MM2 is the molar mass for gas1 and gas 2.
Answer to Problem 79QAP
The average kinetic average translational energy of CH4 in tank C is EQ the average kinetic average translational energy of SO2 in tank A.
Explanation of Solution
Now we know that according to the ideal gas law the value of the average translational kinetic energy is determined as below:
Here,
Et = average translational energy of gas
T = temperature in Kelvin
R = Universal gas constant
NA = Avogadro number
Because, the temperature is also constant. So, both the gases will contain similar average kinetic average translational energy.
Therefore, the average kinetic average translational energy of CH4 in tank C is EQ the average kinetic average translational energy of SO2 in tank A.
(c)
Interpretation:
The effusion time of SO2 from Tank A 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 time1 and time2 is the time of effusion for gas1 and gas 2. MM1 and MM2 is the molar mass for gas1 and gas 2.
Answer to Problem 79QAP
Time taken by total of SO2 gas to effuse out of tank from an identical hole is LT 40s.
Explanation of Solution
As per the Graham’s law of effusion (at constant P and T) is as below:
Here MO2 is the molar mass of oxygen gas and MSO2 is the molar mass of Sulphur dioxide gas
Putting the values:
Thus, of O2 gas take 20 Sec to effuse then the time taken by SO2 gas to effuse:
Therefore, time taken by total of SO2 gas to effuse out of tank from an identical hole is LT 40s.
(d)
Interpretation:
The gas from O2 and CH4, with higher density 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 time1 and time2 is the time of effusion for gas1 and gas 2. MM1 and MM2 is the molar mass for gas1 and gas 2.
Answer to Problem 79QAP
For both the gases average translational energies are same.
Explanation of Solution
The expression of the density is as below:
Here M is the molar mass and V is volume.
Thus, when volume is constant then density is directly proportional to molar mass so as greater the molar mass greater will be the density:
Now in case of O2 and CH4
Thus, molar mass of oxygen is greater than the molar lass of methane gas.
Therefore, the densities of O2 in tank B is GT the densities of gas CH4 in tank C.
(e)
Interpretation:
The tank between A and B with higher pressure 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, time1 and time2 is the time of effusion for gas1 and gas 2. MM1 and MM2 is the molar mass for gas1 and gas 2.
Answer to Problem 79QAP
For both the gases average translational energies are same.
Explanation of Solution
According to the ideal gas equation:
If n, V is constant as in the question, then T is directly proportional to pressure so:
Here, TA and TB are the temperatures of Tank A and B while PA and PB is the pressure of Tank A and B.
Putting the values of TA and TB
Thus, the pressure in tank A is GT half the pressure in tank B.
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Chapter 5 Solutions
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