Question

How many gram of ${\text{C}}{{\text{O}}_{\text{2}}}$ would be needed to have the same number of moles of ${\text{C}}{{\text{O}}_{\text{2}}}$ as there are in ${\text{52}}{\text{.2}}$ grams of ${{\text{H}}_2}{\text{O}}$?

Answer 1

Hint: The mass of water is also given so we can calculate the moles of water by using mole formula. It is given that moles of carbon dioxide and water are the same. So, we can use the moles of water as the moles of carbon dioxide. By using mole formula we can determine the mass of carbon dioxide.

Complete step by step solution:
We will use the mole formula to determine the number of moles of water as follows:
${\text{mole}}\,{\text{ = }}\,\dfrac{{{\text{mass}}}}{{{\text{molar}}\,{\text{mass}}}}$
Molar mass of water is $18.01$ g/mol.
On substituting $52.2$ grams for mass of water and $18.01$for molar mass of water,
${\text{mole}}\,{\text{ = }}\,\dfrac{{52.2}}{{18.01}}$
${\text{mole}}\,{\text{ = }}2.89$
So, the moles of the water is $2.89$.
It is given that ${\text{C}}{{\text{O}}_{\text{2}}}$have the same number of moles of as there are in ${\text{52}}{\text{.2}}$ grams of ${{\text{H}}_2}{\text{O}}$. So, the number of moles of ${\text{C}}{{\text{O}}_{\text{2}}}$ is also $2.89$ mol.
We will use the mole formula to determine the mass of ${\text{C}}{{\text{O}}_{\text{2}}}$ as follows:
${\text{mole}}\,{\text{ = }}\,\dfrac{{{\text{mass}}}}{{{\text{molar}}\,{\text{mass}}}}$
Molar mass of ${\text{C}}{{\text{O}}_{\text{2}}}$is $44.00$ g/mol.
On substituting $2.89$ mol for moles of ${\text{C}}{{\text{O}}_{\text{2}}}$and $44.00$for molar mass of${\text{C}}{{\text{O}}_{\text{2}}}$,
${\text{2}}{\text{.89}}\,{\text{mol}}\,{\text{ = }}\,\dfrac{{{\text{mass}}}}{{{\text{44}}{\text{.00}}\,{\text{g/mol}}}}$
${\text{mass}}\, = \,{\text{2}}{\text{.89}}\,{\text{mol}}\,\, \times \,{\text{44}}{\text{.00}}\,{\text{g/mol}}$
${\text{mass}}\, = \,127.53\,{\text{g}}$
So, the mass of ${\text{C}}{{\text{O}}_{\text{2}}}$is $127.53$ grams.
So, $127.53$ grams of ${\text{C}}{{\text{O}}_{\text{2}}}$ would be needed to have the same number of moles of ${\text{C}}{{\text{O}}_{\text{2}}}$ as there are in ${\text{52}}{\text{.2}}$ grams of ${{\text{H}}_2}{\text{O}}$.
Therefore, $127.53$ grams is the correct answer.

Note: The number of atoms present in $12\,{\text{g}}$ of carbon-12 is known as one mole. The molar mass of water is the sum of atomic mass of two hydrogen atoms and one oxygen atom. The molar mass of carbon dioxide is the sum of atomic mass of one carbon atom and two oxygen atoms. The unit of molar mass is gram per mole. The unit of mass is gram.