Concept explainers
(a)
Interpretation:
The tank with greater number of moles 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 78QAP
Number of moles of CO2 and H2 are same.
Explanation of Solution
The gas 1 is taken as CO2 and gas 2 as H2 . For both the gases pressure, volume and temperatures are equal. These values are substituted in combined gas la to determine moles of CO2 and H2 as below:
Thus, the number of moles of CO2 and H2 are same.
(b)
Interpretation:
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 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 78QAP
Density of CO2 is higher than H2.
Explanation of Solution
The molar mas of CO2 = 44 g/mol and H2 = 2g/mol
Thus, MM1 = 44 g/mol, and MM2 = 2 g/mol
The ratio of densities of CO2 and H2 is determined as below:
Therefore, the density of CO2 is higher compare to the density of H2.
(c)
Interpretation:
The gas with higher effusion time 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 78QAP
Time of effusion of CO2 will be higher than H2.
Explanation of Solution
The molar mas of CO2 = 44 g/mol and H2 = 2g/mol
The rate of effusion is dependent on the molar mass. The effusion rate for gas with high molar mass will be less. Thus, time of effusion of CO2 will be higher than that of H2.
(d)
Interpretation:
The gas with large average translational 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 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 78QAP
For both the gases average translational energies are same.
Explanation of Solution
The only variable in the equation is temperature. The temperatures for both the gases, CO2 and H2 are same. Th ratio of average translation energy of CO2 and H2 is calculated as below:
Thus, for both the gases CO2 and H2 the average translational energies are same.
(e)
Interpretation:
The gas with more partial pressure on addition of 1 mole of helium in each of the tanks 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 78QAP
Partial pressure for CO2 and H2 is same.
Explanation of Solution
The partial pressure of the gas is the pressure exerted by gas alone. As per the ideal gas equation:
Here partial pressure of gas 1 is P1, n1 is the number of moles of gas 1, V is the volume, T is the temperature and R is the universal gas constant
The number of moles of CO2 and H2 are same. Thus, the number of moles in tank after adding equal amount of He moles to both the tanks containing CO2 and H2 will be same. Also, volume as well as temperature are same of both the gases.
The ratio of partial pressure of tank having CO2 (i.e. P1 ) and H2 (i.e. P2 ) is determined as below:
Thus, partial pressure for CO2 and H2 are same.
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