Pressure of 1 g of an ideal gas A 27°C is found to be 2 bar. When 2 g of another ideal gas B is introduced in the same flask at the same temperature the pressure becomes 3 bar. Find a relationship between their molecular masses.

Asked by Pragya Singh | 1 year ago |  79

1 Answer

Solution :-

For ideal gas A, the ideal gas equation is given by,

\( p_{X}V = n_{X}RT\)……(1)

Where \( p_{X}\)​ and \( n_{X}\)​ represents the pressure and number of moles of gas X.

For ideal gas Y, the ideal gas equation is given by,

\( p_{Y}V = n_{Y}RT\)……(2)

Where, \( p_{Y}\)​ and \( n_{Y}\)​ represent the pressure and number of moles of gas Y.

[V and T are constants for gases X and Y]

From equation (1),

\( p_{ X }V = \dfrac{m_{ X }}{M_{ X }}\)

\( \dfrac{p_{ X }M_{ X }}{m_{ X }}= \dfrac{ R T}{ V }\)​ ……(3)

From equation (2),

\( p_{ Y }V =\dfrac{m_{ Y }}{M_{ Y }}=RT\)

\( \dfrac{p_{ Y }M_{ Y }}{m_{ Y }}= \dfrac{ R T}{V}\) …… (4)

Where, \( M_{ X }\) and \( M_{ Y }\)​ are the molecular masses of gases X and Y respectively.

Now, from equation (3) and (4),

\( \dfrac{p_{ X }M_{ X }}{m_{ X }}= \dfrac{p_{ Y }M_{ Y }}{m_{ Y }}\)​​ ….. (5)

Given,

\( m_{ X }\)= 1 g

\( p_{ X }\)= 2 bar

\( m_{ Y }\)= 2 g

\( p_{ Y }\) = (3 – 2) = 1 bar (Since total pressure is 3 bar)

Substituting these values in equation (5),

\( \dfrac{2 \; \times \; M_{X} }{1}= \dfrac{1 \; \times \; M_{Y} }{2}​​\)

\( 4 M_{ X } = M_{ Y }\)

Therefore, the relationship between the molecular masses of X and Y is,

\( 4 M_{ X }= M_{ Y }\)

Answered by Abhisek | 1 year ago

Related Questions

Critical temperature for carbon dioxide and methane are 31.1°C and – 81.9°C respectively. Which of these has stronger intermolecular forces and why?

Class 11 Chemistry States of Matter View Answer

In terms of Charles’ law explain why -273°C is the lowest possible temperature.

Class 11 Chemistry States of Matter View Answer

A mixture of dihydrogen and dioxygen at one bar pressure contains 20% by weight of dihydrogen. Calculate the partial pressure of dihydrogen.

Class 11 Chemistry States of Matter View Answer