A 300 mL bottle of soft drink has 0.2 M CO2 dissolved in it. Assu… — Solution | JEE Chemistry

NVAEasyJEE 2023Stoichiometry & Calculations

A $300 \, \text{mL}$ bottle of soft drink has $0.2 \, \text{M}$ $CO_2$ dissolved in it. Assuming $CO_2$ behaves as an ideal gas, the volume of the dissolved $CO_2$ at STP is _____ $\text{mL}$ . (Nearest integer)

Given: At STP, molar volume of an ideal gas is $22.7 \, \text{L mol}^{-1}$ .

Answer

Correct answer:1362

Step-by-step solution

Standard Method

Given: Volume of soft drink = $300 \, \text{mL} = 0.300 \, \text{L}$ , molarity of dissolved $CO_2$ = $0.2 \, \text{mol L}^{-1}$ .

Find: Volume of dissolved $CO_2$ at STP.

Use molarity to find moles of dissolved $CO_2$ :

n = M \times V = 0.2 \times 0.300 = 0.060 \; \text{mol}

At STP, molar volume = $22.7 \, \text{L mol}^{-1}$ . Therefore,

V = n \times 22.7 = 0.060 \times 22.7 = 1.362 \; \text{L}

Converting to millilitres,

1.362 \; \text{L} = 1362 \; \text{mL}

Therefore, the volume of dissolved $CO_2$ at STP is $1362 \, \text{mL}$ .

The solution appears unrelated to this question, so the answer is derived from the question data and given correct answer field.

Common mistakes

Using $300$ directly in the molarity formula as litres is incorrect because molarity is in $\text{mol L}^{-1}$ . First convert $300 \, \text{mL}$ to $0.300 \, \text{L}$ .
Multiplying by molar volume before finding moles is incorrect. First calculate moles of dissolved $CO_2$ using $n = MV$ , then convert those moles to gas volume at STP.
Leaving the final answer in litres is incomplete because the question asks for $\text{mL}$ . After obtaining $1.362 \, \text{L}$ , convert it to $1362 \, \text{mL}$ .

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