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Pressure of 1 G of an Ideal Gas a at 27 °C is Found to Be 2 Bar. When 2 G of Another Ideal Gas B is Introduced in the Same Flask at Same Temperature the Pressure Becomes 3 Bar. Find a Relationship Between Their Molecular Masses. - CBSE (Science) Class 11 - Chemistry

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Question

The pressure of 1 g of an ideal gas A at 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.

Solution 1

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

`P_AV =  n_ART`  ............(i)

Where, pA and nA represent the pressure and number of moles of gas A.

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

`p_sV = n_sRT`  ......(ii)

Where, pand nB represent the pressure and number of moles of gas B.

[V and T are constants for gases A and B]

From equation (i), we have

`p_AV = m_A/M_A RT => (p_AM_A)/m_A  = (RT)/V`   .....(iii)

From equation (ii), we have

`p_BV = m_B/M_B RT => (p_BM_B)/m_B = RT/V` .......(iv)

Where, Mand MB are the molecular masses of gases A and B respectively.

Now, from equations (iii) and (iv), we have

`(p_M_A)/m_A = (p_BM_B)/m_B`  .....(v)

Given

`m_A = 1 g`

`p_A =  2 "bar"`

`m_B = 2g`

`p_B = (3 -2) = 1 "bar"`

(Since total pressure is 3 bar)

Substituting these values in equation (v), we have

`(2xxM_A)/1 = (1xxM_B)/2`

`=> 4M_A = M_B`

Thus, a relationship between the molecular masses of A and B is given by

`4M_A = M_B`

 

 

Solution 2

Suppose molecular masses of A and B are MA and MB respectively. Then their number of moles will be

`n_A = 1/M_A` , `n_B= 2/M_B`

`P_A =  "2bar", P_A + P_B =  3 bar, i.e P_B =  1 "bar"`

Applying the relation PV = nRT

`P_AV = n_ART`, `P_BV = n_BRT`

`:. P_A/P_B = n_A/n_B = (1/M_A)/(2/M_B) = M_B/(2M_A)`

or `M_B/M_A =  2xx P_A/P_B = 2 xx 2/1  =\ 4 or M_B =  4 M_A`

  Is there an error in this question or solution?

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Solution Pressure of 1 G of an Ideal Gas a at 27 °C is Found to Be 2 Bar. When 2 G of Another Ideal Gas B is Introduced in the Same Flask at Same Temperature the Pressure Becomes 3 Bar. Find a Relationship Between Their Molecular Masses. Concept: Laws of Chemical Combination - Avogadro Law.
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