in the reaction c + o₂ → co₂, 18 g of carbon react with oxygen to produce 72 g of carbon dioxide. what mass…

Answer:

B. 54 g

Explanation:

Step1: Write the chemical equation

$C + O_2\rightarrow CO_2$

Step2: Calculate molar masses

Molar mass of $C$ is 12 g/mol, molar mass of $O_2$ is 32 g/mol, molar mass of $CO_2$ is 44 g/mol.

Step3: Determine moles of $CO_2$ produced

Moles of $CO_2=\frac{72\ g}{44\ g/mol}\approx1.64\ mol$

Step4: Determine moles of $C$ used

From the equation, mole - ratio of $C$ to $CO_2$ is 1:1. Moles of $C$ used $=\frac{18\ g}{12\ g/mol} = 1.5\ mol$

Step5: Determine moles of $O_2$ needed

Mole - ratio of $O_2$ to $CO_2$ is 1:1. Moles of $O_2$ needed for 1.64 mol of $CO_2$ is also 1.64 mol. But considering the limiting - reactant concept, since moles of $C$ is 1.5 mol, moles of $CO_2$ produced is limited by $C$. Moles of $O_2$ needed is 1.5 mol.

Step6: Calculate mass of $O_2$

Mass of $O_2=moles\times molar\ mass = 1.5\ mol\times32\ g/mol = 48\ g$ (There is an error in the above steps. Let's use the law of conservation of mass.) According to the law of conservation of mass, mass of reactants = mass of products. Let the mass of oxygen be $x$. We know mass of carbon is 18 g and mass of carbon - dioxide is 72 g. So, $18\ g+x = 72\ g$. Solving for $x$, we get $x=72 - 18=54\ g$.