Question

q 29. a student burns 1.50 mol c₃h₈ according to the following reaction: c₃h₈ + 5o₂ → 3co₂ + 4h₂o how many grams of carbon dioxide are produced? options: 1.32×10⁴ g, 6.61×10¹ g, 4.40×10¹ g, 1.98×10² g (note: the original options might have typographical errors in exponents, corrected for clarity)

Explanation:

Step1: Determine mole ratio

From the reaction \( \ce{C3H8 + 5O2 -> 3CO2 + 4H2O} \), 1 mol of \( \ce{C3H8} \) produces 3 mol of \( \ce{CO2} \). For 1.50 mol of \( \ce{C3H8} \), moles of \( \ce{CO2} \) = \( 1.50\space mol\times3 = 4.50\space mol \).

Step2: Calculate molar mass of \( \ce{CO2} \)

Molar mass of \( \ce{C} = 12.01\space g/mol \), \( \ce{O} = 16.00\space g/mol \). So, \( M(\ce{CO2}) = 12.01 + 2\times16.00 = 44.01\space g/mol \).

Step3: Find mass of \( \ce{CO2} \)

Mass = moles × molar mass = \( 4.50\space mol\times44.01\space g/mol \approx 198\space g = 1.98\times10^{2}\space g \)? Wait, no, wait. Wait, maybe I miscalculated the options. Wait, the options have \( 1.98\times10^{2} \)? Wait, no, the options are \( 1.32\times10^{2} \), \( 6.61\times10^{1} \), \( 4.40\times10^{1} \), \( 1.98\times10^{2} \)? Wait, no, the original problem's options: let's recheck. Wait, the reaction is \( \ce{C3H8 + 5O2 -> 3CO2 + 4H2O} \). Moles of \( \ce{C3H8} = 1.50\space mol \). Moles of \( \ce{CO2} = 1.50\times3 = 4.50\space mol \). Mass of \( \ce{CO2} = 4.50\space mol\times44.01\space g/mol = 198\space g = 1.98\times10^{2}\space g \). Wait, but the options have \( 1.98\times10^{2}\space g \)? Wait, maybe the options were typed with a typo, but among the given options, \( 1.98\times10^{2}\space g \) (if the option is \( 1.98\times10^{2}\space g \), but in the image, one option is \( 1.98\times10^{2}\space g \)? Wait, the user's image shows options: \( 1.32\times10^{2}\space g \), \( 6.61\times10^{1}\space g \), \( 4.40\times10^{1}\space g \), \( 1.98\times10^{2}\space g \). Wait, my calculation: 1.50 mol \( \ce{C3H8} \) gives 1.50×3 = 4.50 mol \( \ce{CO2} \). 4.50×44.01 = 198 g = 1.98×10² g. So the correct option is the one with \( 1.98\times10^{2}\space g \) (assuming the option is that). Wait, maybe I made a mistake in the reaction. Wait, the reaction is \( \ce{C3H8 + 5O2 -> 3CO2 + 4H2O} \). Yes. So moles of \( \ce{CO2} \) is 3 times moles of \( \ce{C3H8} \). So 1.50×3 = 4.50 mol. Mass = 4.50×44 = 198 g = 1.98×10² g. So the correct option is the one with \( 1.98\times10^{2}\space g \).

Answer:

The correct option is the one with \( 1.98\times10^{2}\space g \) (assuming the option is labeled as, for example, D. \( 1.98\times10^{2}\space g \)). Wait, in the image, the last option is \( 1.98\times10^{2}\space g \) (probably a typo in the exponent, maybe \( 10^{2} \) instead of \( 10^{8} \) as maybe a typo). So the answer is the option with \( 1.98\times10^{2}\space g \) (the last option in the given choices).