Answer
417.9k+ views
Hint: The pressure exerted by a gas depends on volume, temperature and amount of a gas. This is expressed in the form of gas laws of ideal gases which are known as Boyle’s law, Charles’s law and Avogadro’s law.
Complete step by step answer:
According to the kinetic theory of gases, the particles of the gas are in random motion colliding with each other and with the walls of the container. The collisions are elastic in nature and no kinetic energy of the particles is lost. The pressure of a gas is thus explained with the kinetic theory of gases.
Based on the postulates of kinetic theory of gas three laws were proposed relating the pressure, volume, temperature and number of moles (amount of gas) of gas.
Boyle’s law indicates the volume of a gas is inversely proportional to the pressure. Charles’s law indicates the volume of a gas is directly proportional to the temperature. Avogadro’s law indicates the volume of a gas is directly proportional to the moles of gas.
Combining the three laws leads to a general mathematical equation which is known as the ideal gas equation. The equation is
$PV = nRT$ where \[P\] is pressure, \[V\] is volume, \[n\] is moles of gas, \[R\] is gas constant and \[T\] is absolute temperature.
The density (\[d\]) of a gas is equal to the ratio of molar mass (\[M\]) and volume of gas.
Thus \[d = \dfrac{M}{V}\] or \[V = \dfrac{M}{d}\]
Thus the ideal gas equation is \[PM = dRT\],
Inserting the values for gas \[A\] and\[B\] ,
${P_A} = \dfrac{{{d_A}RT}}{{{M_A}}} = \dfrac{{3RT}}{{{M_A}}}$
$\Rightarrow {P_B} = \dfrac{{{d_B}RT}}{{{M_B}}} = \dfrac{{1.5RT}}{{{M_B}}}$
Therefore, $\dfrac{{PA}}{{PB}} = \dfrac{{\dfrac{{3RT}}{{{M_A}}}}}{{\dfrac{{1.5RT}}{{{M_B}}}}} = \dfrac{{2{M_B}}}{{{M_A}}}$
Given, \[{M_A} = \dfrac{1}{2}{M_B}\]
Thus \[\dfrac{{{P_A}}}{{{P_B}}} = \dfrac{{2{M_B}}}{{\dfrac{1}{2}{M_B}}} = 4\] .
So, the correct answer is Option C.
Note: The gases which show deviation from ideal gas behaviour are known as real gases. The pressure of the gas is referred to as the force of colliding particles per unit area. Thus the pressure of a gas is directly proportional to the frequency of collisions per unit time and area of the container.
Complete step by step answer:
According to the kinetic theory of gases, the particles of the gas are in random motion colliding with each other and with the walls of the container. The collisions are elastic in nature and no kinetic energy of the particles is lost. The pressure of a gas is thus explained with the kinetic theory of gases.
Based on the postulates of kinetic theory of gas three laws were proposed relating the pressure, volume, temperature and number of moles (amount of gas) of gas.
Boyle’s law indicates the volume of a gas is inversely proportional to the pressure. Charles’s law indicates the volume of a gas is directly proportional to the temperature. Avogadro’s law indicates the volume of a gas is directly proportional to the moles of gas.
Combining the three laws leads to a general mathematical equation which is known as the ideal gas equation. The equation is
$PV = nRT$ where \[P\] is pressure, \[V\] is volume, \[n\] is moles of gas, \[R\] is gas constant and \[T\] is absolute temperature.
The density (\[d\]) of a gas is equal to the ratio of molar mass (\[M\]) and volume of gas.
Thus \[d = \dfrac{M}{V}\] or \[V = \dfrac{M}{d}\]
Thus the ideal gas equation is \[PM = dRT\],
Inserting the values for gas \[A\] and\[B\] ,
${P_A} = \dfrac{{{d_A}RT}}{{{M_A}}} = \dfrac{{3RT}}{{{M_A}}}$
$\Rightarrow {P_B} = \dfrac{{{d_B}RT}}{{{M_B}}} = \dfrac{{1.5RT}}{{{M_B}}}$
Therefore, $\dfrac{{PA}}{{PB}} = \dfrac{{\dfrac{{3RT}}{{{M_A}}}}}{{\dfrac{{1.5RT}}{{{M_B}}}}} = \dfrac{{2{M_B}}}{{{M_A}}}$
Given, \[{M_A} = \dfrac{1}{2}{M_B}\]
Thus \[\dfrac{{{P_A}}}{{{P_B}}} = \dfrac{{2{M_B}}}{{\dfrac{1}{2}{M_B}}} = 4\] .
So, the correct answer is Option C.
Note: The gases which show deviation from ideal gas behaviour are known as real gases. The pressure of the gas is referred to as the force of colliding particles per unit area. Thus the pressure of a gas is directly proportional to the frequency of collisions per unit time and area of the container.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)