Final Answer:
Approximately 250 grams of C₃H₈ can be produced from 2.3 kg of CH₄.
To find the answer, use the molar ratios between CH₄ and C₃H₈. 2.3 kg of CH₄ is first converted to grams (2300 grams). Then, by using the molar ratio between CH₄ and C₃H₈, you find the number of moles of CH₄ and then convert that to grams of C₃H₈.
Step-by-step explanation:
To start, convert the given mass of CH₄ from kilograms to grams:
2.3 kg * 1000 grams/kg = 2300 grams of CH₄
Next, use the balanced chemical equation for the reaction involving CH₄ and C₃H₈. The balanced equation is:
CH₄ → C₃H₈
From the balanced equation, it's known that 1 mole of CH₄ produces 1 mole of C₃H₈.
Find the number of moles of CH₄:
Molar mass of CH₄ = 12.01 (C) + 4(1.008) (H) = 16.04 g/mol
Number of moles of CH₄ = Mass / Molar mass = 2300 g / 16.04 g/mol ≈ 143.5 moles
As per the stoichiometry of the balanced equation, every mole of CH₄ results in the production of 1 mole of C₃H₈. Therefore, the number of moles of C₃H₈ produced is also approximately 143.5 moles.
Convert moles of C₃H₈ to grams:
Molar mass of C₃H₈ = 3(12.01) + 8(1.008) = 44.1 g/mol
Mass of C₃H₈ = Number of moles * Molar mass = 143.5 moles * 44.1 g/mol ≈ 6322.85 g ≈ 6323 g ≈ 6.32 kg
Finally, round the calculated mass to the appropriate significant figures, considering the original data provided and the molar masses involved:
Approximately 6.32 kg of C₃H₈ can be produced from 2.3 kg of CH₄.