Question

Assertion Reason:
Statement -1 : Molality of pure ethanol is lesser than pure water.
Statement -2 : As density of ethanol is lesser than density of water.
[Given : dethanol = 0.789 gm/ml; dwater = 1 gm/ml]
(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.
(B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.
(C) Statement-1 is false, statement-2 is true.
(D) Statement-1 is true, statement-2 is false.

Answer 1

ANSWER:

• (B) Statement - 1 is true, statement - 2 is true and statement - 2 is not the correct explanation for statement - 1.

GIVEN:

• Statement - 1 : Molality of pure ethanol is lesser than pure water.

• Statement - 2 : As density of ethanol is lesser than density of water.

TO VERIFY:

• The given statements.

EXPLANATION:

$\bigstar \ \boxed{ \large{\bold{ \orange{Molality =\dfrac{Moles\ of\ solute}{Mass\ of \ solvent}}}}}$

$\sf\implies Let \ m_e\ be \ the \ molality \ of \ ethanol.$

$\sf \implies Let \ m_w\ be \ the \ molality \ of \ water.$

$\sf\implies Let \ the\ mass\ of \ solvent \ be \ the\ same.$

$\bigstar \ \boxed{ \large{\bold{ \green{Moles=\dfrac{Mass}{Molecular \ mass}}}}}$

$\sf \dashrightarrow m_e =\dfrac{ \bigg( \dfrac{Mass \ of \ ethanol}{Molecular \ mass} \bigg) }{Mass\ of \ solvent}$

$\bigstar \ \boxed{ \large{\bold{ \red{Mass = Density \times Volume}}}}$

$\sf \dashrightarrow m_e =\dfrac{ \bigg( \dfrac{0.789 \times v}{Molecular \ mass} \bigg) }{Mass\ of \ solvent}$

$\sf \dashrightarrow m_e =\dfrac{ \bigg( \dfrac{0.789 \times v}{46} \bigg) }{Mass\ of \ solvent}$

$\sf\implies Let \ the\ volume \ be \ the\ same.$

$\sf\dashrightarrow Similarly, \ m_w =\dfrac{ \bigg( \dfrac{1 \times v}{Molecular \ mass} \bigg) }{Mass\ of \ solvent}$

$\sf\dashrightarrow m_w =\dfrac{ \bigg( \dfrac{1 \times v}{18} \bigg) }{Mass\ of \ solvent}$

$\sf \dashrightarrow \dfrac{m_e}{m_w} = \dfrac{\dfrac{ \bigg( \dfrac{0.789 \times v}{46} \bigg) }{Mass\ of \ solvent} }{\dfrac{ \bigg( \dfrac{1 \times v}{18} \bigg) }{Mass\ of \ solvent}}$

$\sf \dashrightarrow \dfrac{m_e}{m_w} = \dfrac{\dfrac{ 0.789 \times v}{46} }{\dfrac{ v}{18} }$

$\sf \dashrightarrow \dfrac{m_e}{m_w} = \dfrac{\dfrac{ 0.789 }{46}}{\dfrac{ 1}{18} }$

$\sf \dashrightarrow \dfrac{m_e}{m_w} = \dfrac{0.789 \times 18 }{46}$

$\sf \dashrightarrow \dfrac{m_e}{m_w} = \dfrac{14.202 }{46}$

$\sf \dashrightarrow \dfrac{m_e}{m_w} = 0.309$

$\sf \dashrightarrow m_e= 0.309 \ m_w$

$\bigstar \ \sf \blue{Statement\ 1\ is\ correct\ m_e < m_w}$

$\bigstar\ \sf \purple{Statement\ 2\ is\ correct\ (1 > 0.789)}$

REASON:

• Eventhough density is smaller for ethanol, molecular mass influences greatly the molality of ethanol and water.

• Because difference between molecular masses of ethanol are much greater when compared to difference between densities.

• Also generally, density is not used to calculate the molality.