1.

@ Moderators@ Stars @ Best UsersDefine Molarity and Molality Derive the relation between them ​

Answer» <html><body><h3>♣ Definitions :-</h3><p></p><p></p><p><strong>♠》 <u>Molarity</u> (M) :-</strong></p><p></p><p>It is the number of moles of <a href="https://interviewquestions.tuteehub.com/tag/solute-1217068" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTE">SOLUTE</a> dissolved in one litre of solution.</p><p><img align="absmiddle" alt="\bf M = \dfrac{n_2 }{V_{sol.}(in \:L)} \\ \\ \bf M= \dfrac{n_2 }{V_{sol.}(in \:mL)} \times 1000" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?f=%20%5Cbf%20M%20%3D%20%5Cdfrac%7Bn_2%20%7D%7BV_%7Bsol.%7D%28in%20%5C%3AL%29%7D%20%20%5C%5C%20%20%5C%5C%20%20%5Cbf%20M%3D%20%5Cdfrac%7Bn_2%20%7D%7BV_%7Bsol.%7D%28in%20%5C%3AmL%29%7D%20%5Ctimes%201000" title="\bf M = \dfrac{n_2 }{V_{sol.}(in \:L)} \\ \\ \bf M= \dfrac{n_2 }{V_{sol.}(in \:mL)} \times 1000"/></p><p></p><p></p><p><strong>♠》 <a href="https://interviewquestions.tuteehub.com/tag/molality-562964" style="font-weight:bold;" target="_blank" title="Click to know more about MOLALITY">MOLALITY</a> (m) :-</strong></p><p></p><p>It is the number of moles of solute dissolve in one kg of Solvent.</p><p><img align="absmiddle" alt="\bf m = \dfrac{n_2 }{W_1(in \:kg)} \\ \\ \bf m = \dfrac{n_2 }{ W_1(in \:g)} \times 1000" class="latex-formula" id="TexFormula2" src="https://tex.z-dn.net/?f=%5Cbf%20m%20%3D%20%5Cdfrac%7Bn_2%20%7D%7BW_1%28in%20%5C%3Akg%29%7D%20%20%5C%5C%20%20%5C%5C%20%5Cbf%20m%20%3D%20%5Cdfrac%7Bn_2%20%7D%7B%20W_1%28in%20%5C%3Ag%29%7D%20%5Ctimes%201000" title="\bf m = \dfrac{n_2 }{W_1(in \:kg)} \\ \\ \bf m = \dfrac{n_2 }{ W_1(in \:g)} \times 1000"/></p><p></p><h2><u>-----------------------</u></h2><p><strong>♣ Relation b/<a href="https://interviewquestions.tuteehub.com/tag/w-729065" style="font-weight:bold;" target="_blank" title="Click to know more about W">W</a> Molarity and Molality :-</strong></p><p></p><p><img align="absmiddle" alt="\large \purple{ \underline {\boxed{{\bf \frac{d}{ M } = \frac{1}{m} + \frac{M_2}{1000} }}}}" class="latex-formula" id="TexFormula3" src="https://tex.z-dn.net/?f=%5Clarge%20%5Cpurple%7B%20%5Cunderline%20%7B%5Cboxed%7B%7B%5Cbf%20%20%5Cfrac%7Bd%7D%7B%20M%20%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7Bm%7D%20%2B%20%5Cfrac%7BM_2%7D%7B1000%7D%20%7D%7D%7D%7D" title="\large \purple{ \underline {\boxed{{\bf \frac{d}{ M } = \frac{1}{m} + \frac{M_2}{1000} }}}}"/></p><p></p><h2><u>-----------------------</u></h2><h3>♣ Derivation :-</h3><p></p><p><strong><u>We have</u></strong> ,</p><p></p><p><img align="absmiddle" alt="\sf m = \dfrac{n_2 }{ W_1(in \:g)} \times 1000 \: \: \:. \: . \: . \: \{i \} \\ \\ \bf and \\ \\ \sf M = \dfrac{n_2 }{V_{sol.}(in \:mL)} \times 1000 \: \: \: .\: . \: . \: \{ii \}" class="latex-formula" id="TexFormula4" src="https://tex.z-dn.net/?f=%20%5Csf%20m%20%3D%20%5Cdfrac%7Bn_2%20%7D%7B%20W_1%28in%20%5C%3Ag%29%7D%20%5Ctimes%201000%20%5C%3A%20%5C%3A%20%5C%3A.%20%5C%3A%20.%20%5C%3A%20.%20%5C%3A%20%5C%7Bi%20%5C%7D%20%5C%5C%20%5C%5C%20%5Cbf%20and%20%5C%5C%20%5C%5C%20%5Csf%20M%20%3D%20%5Cdfrac%7Bn_2%20%7D%7BV_%7Bsol.%7D%28in%20%5C%3AmL%29%7D%20%5Ctimes%201000%20%5C%3A%20%5C%3A%20%5C%3A%20.%5C%3A%20.%20%5C%3A%20.%20%5C%3A%20%5C%7Bii%20%5C%7D" title="\sf m = \dfrac{n_2 }{ W_1(in \:g)} \times 1000 \: \: \:. \: . \: . \: \{i \} \\ \\ \bf and \\ \\ \sf M = \dfrac{n_2 }{V_{sol.}(in \:mL)} \times 1000 \: \: \: .\: . \: . \: \{ii \}"/></p><p></p><h3> <u>Dividing</u> {i} <u>by</u> {ii} <u>We Get, </u></h3><p></p><p><img align="absmiddle" alt="\sf\dfrac{m}{ M} = \dfrac{V_{sol.}}{W_1} \\ \\ \sf = \frac{W_{sol.}/d}{W_1} \\ \\ \sf = \frac{W_1 + W_2}{d.W_1}" class="latex-formula" id="TexFormula5" src="https://tex.z-dn.net/?f=%20%5Csf%5Cdfrac%7Bm%7D%7B%20M%7D%20%3D%20%5Cdfrac%7BV_%7Bsol.%7D%7D%7BW_1%7D%20%5C%5C%20%5C%5C%20%5Csf%20%3D%20%5Cfrac%7BW_%7Bsol.%7D%2Fd%7D%7BW_1%7D%20%5C%5C%20%5C%5C%20%5Csf%20%3D%20%5Cfrac%7BW_1%20%2B%20W_2%7D%7Bd.W_1%7D%20" title="\sf\dfrac{m}{ M} = \dfrac{V_{sol.}}{W_1} \\ \\ \sf = \frac{W_{sol.}/d}{W_1} \\ \\ \sf = \frac{W_1 + W_2}{d.W_1}"/></p><p></p><p><img align="absmiddle" alt="\sf = \dfrac{1}{d} \bigg \{ \dfrac{W_2}{W_1} + 1 \bigg \} \\ \\ \sf = \dfrac{1}{d} \bigg \{ \frac{n_2}{n_2} \times \dfrac{W_2}{W_1} + 1\bigg \} \\ \\ \sf = \frac{1}{d} \bigg \{ \dfrac{n_2}{W_2 /M_2} \times \dfrac{W_2}{W_1} + 1 \bigg \} \\ \\ \sf = \frac{1}{d} \bigg \{ \frac{n_2.M_2}{W_1} + 1\bigg \}\\\\ \sf = \dfrac{1}{d} \bigg \{ \dfrac{m. M_2 }{1000} + 1 \bigg \} \\" class="latex-formula" id="TexFormula6" src="https://tex.z-dn.net/?f=%5Csf%20%3D%20%5Cdfrac%7B1%7D%7Bd%7D%20%5Cbigg%20%5C%7B%20%5Cdfrac%7BW_2%7D%7BW_1%7D%20%2B%201%20%5Cbigg%20%5C%7D%20%5C%5C%20%5C%5C%20%5Csf%20%3D%20%5Cdfrac%7B1%7D%7Bd%7D%20%5Cbigg%20%5C%7B%20%5Cfrac%7Bn_2%7D%7Bn_2%7D%20%5Ctimes%20%5Cdfrac%7BW_2%7D%7BW_1%7D%20%2B%201%5Cbigg%20%5C%7D%20%5C%5C%20%5C%5C%20%5Csf%20%3D%20%5Cfrac%7B1%7D%7Bd%7D%20%5Cbigg%20%5C%7B%20%5Cdfrac%7Bn_2%7D%7BW_2%20%2FM_2%7D%20%5Ctimes%20%5Cdfrac%7BW_2%7D%7BW_1%7D%20%2B%201%20%5Cbigg%20%5C%7D%20%5C%5C%20%5C%5C%20%5Csf%20%3D%20%5Cfrac%7B1%7D%7Bd%7D%20%5Cbigg%20%5C%7B%20%5Cfrac%7Bn_2.M_2%7D%7BW_1%7D%20%2B%201%5Cbigg%20%5C%7D%5C%5C%5C%5C%20%5Csf%20%3D%20%5Cdfrac%7B1%7D%7Bd%7D%20%5Cbigg%20%5C%7B%20%5Cdfrac%7Bm.%20M_2%20%7D%7B1000%7D%20%2B%201%20%5Cbigg%20%5C%7D%20%5C%5C" title="\sf = \dfrac{1}{d} \bigg \{ \dfrac{W_2}{W_1} + 1 \bigg \} \\ \\ \sf = \dfrac{1}{d} \bigg \{ \frac{n_2}{n_2} \times \dfrac{W_2}{W_1} + 1\bigg \} \\ \\ \sf = \frac{1}{d} \bigg \{ \dfrac{n_2}{W_2 /M_2} \times \dfrac{W_2}{W_1} + 1 \bigg \} \\ \\ \sf = \frac{1}{d} \bigg \{ \frac{n_2.M_2}{W_1} + 1\bigg \}\\\\ \sf = \dfrac{1}{d} \bigg \{ \dfrac{m. M_2 }{1000} + 1 \bigg \} \\"/></p><p></p><p><img align="absmiddle" alt="\large :\longmapsto \purple{ \underline {\boxed{{\bf \frac{d}{ M } = \frac{1}{m} + \frac{M_2}{1000} }}}}" class="latex-formula" id="TexFormula7" src="https://tex.z-dn.net/?f=%5Clarge%20%3A%5Clongmapsto%20%5Cpurple%7B%20%5Cunderline%20%7B%5Cboxed%7B%7B%5Cbf%20%20%5Cfrac%7Bd%7D%7B%20M%20%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7Bm%7D%20%2B%20%5Cfrac%7BM_2%7D%7B1000%7D%20%7D%7D%7D%7D" title="\large :\longmapsto \purple{ \underline {\boxed{{\bf \frac{d}{ M } = \frac{1}{m} + \frac{M_2}{1000} }}}}"/></p><p></p><h3>♣ Notations <a href="https://interviewquestions.tuteehub.com/tag/used-2318798" style="font-weight:bold;" target="_blank" title="Click to know more about USED">USED</a> :-</h3><p></p><ul><li>W = Mass</li></ul><p></p><ul><li>M = Molar Mass</li></ul><p></p><ul><li>1 = Solvent</li></ul><p></p><ul><li>2 = Solute</li></ul><p></p><ul><li>n = number of moles</li></ul><p></p><ul><li>d = density in g/mL.</li></ul><p></p><h2></h2><p></p><p><img align="absmiddle" alt="\LARGE\red{\mathfrak{ \text{W}hich \:\:is\:\: the\:\: required} }\\ \Huge \red{\mathfrak{ \text{ A}nswer.}}" class="latex-formula" id="TexFormula8" src="https://tex.z-dn.net/?f=%20%5CLARGE%5Cred%7B%5Cmathfrak%7B%20%20%5Ctext%7BW%7Dhich%20%5C%3A%5C%3Ais%5C%3A%5C%3A%20the%5C%3A%5C%3A%20required%7D%20%7D%5C%5C%20%5CHuge%20%5Cred%7B%5Cmathfrak%7B%20%5Ctext%7B%20A%7Dnswer.%7D%7D" title="\LARGE\red{\mathfrak{ \text{W}hich \:\:is\:\: the\:\: required} }\\ \Huge \red{\mathfrak{ \text{ A}nswer.}}"/></p><p></p><h2><u>-----------------------</u></h2></body></html>


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