A certain amount of NaOH is dissolved in certain kilograms of solvent and molality of the solution is 0.5 m. When the same amount of NaOH is dissolved in 100 grams of less solvent than initial then molality becomes 0.625 m. Determine the amount of NaOH and the initial mass of solvent.​

NaOH is dissolved in certain kilograms of solvent and molality of solution 0.5m.

Again , same among of NaOH is dissolved in 100 grams of solvent than initial , then molality becomes 0.625m.

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Now lets find the amount of NaOH and the initial mass of solvent.

Let,

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$\sf\bold{ ❍ We\:know,}$

$\sf{Molality(m)=}$ $\sf\dfrac{No.of\:moles\:of\:solute}{No.of\:solvent\:in\:kg}$

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$\sf\bold{Putting\:the\:formula:-}$

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$\sf\huge\underline\bold{ ❍Case:1}$

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$\longmapsto$ $\sf\small{0.5}$ $\sf\dfrac{x}{y}$

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$\longmapsto$ $\sf{0.5y = x }$

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$\longmapsto$ $\sf{multiply\:by\:2→ y = 2x}$

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$\sf\huge\underline\bold{ ❍Case:2}$

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$\longmapsto$ $\sf\small{0.625}$ $\sf\small\dfrac{x}{y}$ = $\sf\dfrac{x}{y=100g}$

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$\longmapsto$ $\sf\small{0.625}$ $\sf\dfrac{x}{y-100/1000kg}$ = $\sf\dfrac{x}{y-0.1kg}$

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$\longmapsto$ $\sf{0.625(y-0.1kg)=x}$

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$\longmapsto$ $\sf{0.625y-0.0625=x}$

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$\sf\small\bold{By\:putting\:the\:value\:of \:"x" we\: get:}$

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$\longmapsto$ $\sf{0.625(2x)-0.0625 = x}$

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$\longmapsto$ $\sf{1.25x 0.0625 = x}$

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$\longmapsto$ $\sf{1.25x - x = 0.0625}$

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$\longmapsto$ $\sf{0.25x = = 0.0625}$

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$\longmapsto$ $\sf\small{x=}$ $\sf\dfrac{0.0625}{0.25}$= $\sf\bold{x=0.25}$

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$\sf{So,y=2(x)=2\times0.25=}$ $\sf\bold{y=0.5}$

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$\sf\small{Initial\:mass\:of\:solvent:0.5kg=500g}$

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$\sf{Now,}$

Amount of NaOH=

$\space$ $\space$ $\space$ $\space$ $\space$ $\sf{=x\times molar\:mass}$

$\space$ $\space$ $\space$ $\space$ $\space$ $\sf{=0.25\times 40=10}$

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$\sf\underline{\underline{ ⚘ Hence,amount\:of\:NaOH=10kg}}$

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number of molecules / avogadro's number * molecule molecular = mass

explanation:

we define a gram-molecular weight as the mass of one mole of any element or compound. a mole contains avogadro's number of units (molecules) –  

6.022

x

10

23

. so, dividing the number of molecules by avogadro's number gives us the number of moles. multiplying that by the molecular weight gives us the mass. from the periodic table we find the gram-molecular weight of u to be238 and of f to be19. so,  

u

f

6

will have a gram-molecular weight of 352g.

u i forgot the answer?