When 9.45g of ClCH₂COOH is added to 500ml. of water, its freezing point drops by 0.5°C. The dissociation constant of ClCH₂ COOH is x × 10^-3. The value of x is__________ (Rounded off to the nearest integer)

$[k_{f (H_{2} O)} = 1.86 K k g m o l^{- 1}]$

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alok kumar singh | Contributor-Level 10

a month ago

$Δ T_{f} = 0.5 ° C$

K_f = 1.86

Using, density of water = 1g / mL

i = ?

$Δ T_{f} = i k_{f} . m$

$0.5 = i \times 1.86 \times \frac{9.45}{94.5 \times 500} \times 1000$

i = 1.344

Now, using $α = \frac{i - 1}{n - 1}$

n for ClCH₂COOH = 2

a = $\frac{1.344 - 1}{2 - 1} = 0.344$

Using

$K_{a} = \frac{C α^{2}}{1 - α}$

$K_{a} = \frac{0.2 \times {(0.344)}^{3}}{0.66} = 36 \times 1 0^{- 3}$

So; x = 36

<math> <mrow> <mi>Δ</mi> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>5</mn> <mo>°</mo> <mi>C</mi> </mrow> </math> Kf = 1.86Using, density of water = 1g / mLi = ?  <math> <mrow> <mi>Δ</mi> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mi>i</mi> <msub> <mrow> <mi>k</mi> </mrow> <mrow> <mi>f</mi> </mrow> </msub> <mo>.</mo> <mi>m</mi> </mrow> </math>             <math> <mrow> <mn>0</mn> <mo>.</mo> <mn>5</mn> <mo>=</mo> <mi>i</mi> <mo>×</mo> <mn>1</mn> <mo>.</mo> <mn>8</mn> <mn>6</mn> <mo>×</mo> <mfrac> <mrow> <mn>9</mn> <mo>.</mo> <mn>4</mn> <mn>5</mn> </mrow> <mrow> <mn>9</mn> <mn>4</mn> <mo>.</mo> <mn>5</mn> <mo>×</mo> <mn>5</mn> <mn>0</mn> <mn>0</mn> </mrow> </mfrac> <mo>×</mo> <mn>1</mn> <mn>0</mn> <mn>0</mn> <mn>0</mn> </mrow> </math>         i = 1.344Now, using <math> <mrow> <mi>α</mi> <mo>=</mo> <mfrac> <mrow> <mi>i</mi> <mo>−</mo> <mn>1</mn> </mrow> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </math>  n for ClCH2COOH = 2a =  <math> <mrow> <mfrac> <mrow> <mn>1</mn> <mo>.</mo> <mn>3</mn> <mn>4</mn> <mn>4</mn> <mo>−</mo> <mn>1</mn> </mrow> <mrow> <mn>2</mn> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>3</mn> <mn>4</mn> <mn>4</mn> </mrow> </math>  Using <math> <mrow> <msub> <mrow> <mi>K</mi> </mrow> <mrow> <mi>a</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mi>C</mi> <msup> <mrow> <mi>α</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mi>α</mi> </mrow> </mfrac> </mrow> </math>   <math> <mrow> <msub> <mrow> <mi>K</mi> </mrow> <mrow> <mi>a</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>0</mn> <mo>.</mo> <mn>2</mn> <mo>×</mo> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mn>0</mn> <mo>.</mo> <mn>3</mn> <mn>4</mn> <mn>4</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>3</mn> </mrow> </msup> </mrow> <mrow> <mn>0</mn> <mo>.</mo> <mn>6</mn> <mn>6</mn> </mrow> </mfrac> <mo>=</mo> <mn>3</mn> <mn>6</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> </math>       So; x = 36

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When 9.45g of ClCH₂COOH is added to 500ml. of water, its freezing point drops by 0.5°C. The dissociation constant of ClCH₂ COOH is x × 10^-3. The value of x is__________ (Rounded off to the nearest integer)

$[k_{f (H_{2} O)} = 1.86 K k g m o l^{- 1}]$

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When 9.45g of ClCH2COOH is added to 500ml. of water, its freezing point drops by 0.5°C. The dissociation constant of ClCH2 COOH is x × 10-3. The value of x is__________ (Rounded off to the nearest integer) [ k f ( H 2 O ) = 1 . 8 6 K k g m o l − 1 ]

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When 9.45g of ClCH₂COOH is added to 500ml. of water, its freezing point drops by 0.5°C. The dissociation constant of ClCH₂ COOH is x × 10^-3. The value of x is__________ (Rounded off to the nearest integer)

$[k_{f (H_{2} O)} = 1.86 K k g m o l^{- 1}]$