Question

What mass of carbon monoxide must be burned to produce 175 kJ of heat under standard state conditions?

Short answer

The mass of carbon dioxide that must be burned is equal to 17.3124 g.

Step-by-step solution

Combustion reaction

Here, we must determine what amount of carbon monoxide must be burned in order to emit 175 kJ of heat.

The reaction of combustion of carbon monoxide is shown below

\[{\bf{CO(g) + }}\frac{{\bf{1}}}{{\bf{2}}}{{\bf{O}}_{\bf{2}}}{\bf{(g) }} \to {\bf{ C}}{{\bf{O}}_{\bf{2}}}{\bf{(g) , \Delta H}}_{\bf{c}}^{\bf{^\circ }}{\bf{ = - 283}}{\bf{.0 kJmo}}{{\bf{l}}^{{\bf{ - 1}}}}\]

Moles of reactants

From the above stoichiometric balanced equation, we can observe that for combustion of 1 mole of carbon monoxide, \[\frac{1}{2}\]mole of oxygen is needed, and the amount of energy released is 283.0 kJ.

Moles of carbon monoxide

We need to follow the steps to find out the no of moles of carbon monoxide required.

\(\begin{aligned}{\rm{ 283kJ heat is produce when 1 mole of carbon monoxide is burnt}}\\{\rm{175kJ heat will be produced when }}\frac{{{\rm{1 mole \times 175 kJ}}}}{{{\rm{283 kJ}}}}{\rm{of carbon monoxide is burnt}}\\{\rm{ = 0}}{\rm{.6183 mol of carbon monoxide }}\end{aligned}\)

Weight of carbon monoxide

To find out the amount of mass of carbon monoxide, follow the steps below.

\[\begin{aligned}{\rm{ Molecular\;mass\;of\;1 \;mole\; of\; carbon \;monoxide\; is \;28 g}}{\rm{.}}\\{\rm{Weight \;of \;0}}{\rm{.6183\; mole \;of\; carbon \;monoxide\; is\; (0}}{\rm{.6183 \times 28)g}}\\{\rm{ = 17}}{\rm{.3124 g}}\end{aligned}\]

Hence, 17.3124 g of carbon monoxide must be burned to produce 175 kJ of heat under standard conditions.