A company dissolves 'X' amount of $\mathrm{CO}_{2}$ at 298 K in 1 litre of water to prepare soda water $\mathrm{X}=$ _____ $\times 10^{-3} \mathrm{~g}$. (nearest integer) (Given: partial pressure of $\mathrm{CO}_{2}$ at $298 \mathrm{~K}=0.835$ bar. Henry's law constant for $\mathrm{CO}_{2}$ at $298 \mathrm{~K}=1.67$ kbar. Atomic mass of H, C and O is 1, 12 and 16 g $\mathrm{mol}^{-1}$, respectively)

JEE Main · 2022 · 24 Jun 2022 · Shift 2 · Solutions

A company dissolves 'X' amount of

CO_{2}

at 298 K in 1 litre of water to prepare soda water

X =

_____

\times 1 0^{- 3} g

. (nearest integer)
(Given: partial pressure of

CO_{2}

298 K = 0.835

bar.

Henry's law constant for

CO_{2}

298 K = 1.67

kbar.
Atomic mass of H, C and O is 1, 12 and 16 g

mol^{- 1}

, respectively)

Answer: 1222

Solution

Using Henry's law:

P = K_{H} χ_{CO_{2}}

. With

P = 0.835

bar,

K_{H} = 1670

bar, and 1 L water (≈1000 g, ≈55.56 mol):

0.835 = 1670 \times \frac{n _{CO_{2}}}{55.56}

. Solving:

n_{CO_{2}} \approx 0.0278

mol. Mass =

0.0278 \times 44 \approx 1.22

g =

1220 \times 1 0^{- 3}

g. (Answer accepts 1221 or 1222.)

JEE Main · 2022 · 24 Jun 2022 · Shift 2 · Integer answer

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