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Current Question (ID: 20836)

Question:

$\text{For a rocket running on fuel (C}_{15}\text{H}_{30}\text{) and liquid oxygen, how much oxygen is required, and}$ $\text{how much CO}_{2}\text{ is released for every liter of fuel, respectively? (Given:}$ $\text{density of the fuel is 0.756 g/mL))}$

Options:

1. $1188 \text{ g and } 1296 \text{ g}$
2. $2376 \text{ g and } 2592 \text{ g}$
3. $2592 \text{ g and } 2376 \text{ g}$
4. $3429 \text{ g and } 3142 \text{ g}$

Solution:

$\text{C}_{15}\text{H}_{30} + \frac{45}{2}\text{O}_{2} \rightarrow 15\text{CO}_{2} + 15\text{H}_{2}\text{O}$ $\text{One litre of fuel has a mass of } (0.756) \times 10 \text{ g.}$ $\therefore \text{ moles of C}_{15}\text{H}_{30} = \frac{756}{210}$ $\text{Moles of O}_{2} \text{ required} = \frac{45}{2} \times \frac{756}{210} \times 32 \text{ g} = 2592 \text{ g}$ $\text{Moles of CO}_{2} \text{ formed} = 15 \times \frac{756}{210} \times 44 = 2376 \text{ g}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}