Respuesta :
Answer: 3.024 g grams of hydrogen are needed to convert 76 grams of chromium(III) oxide, [tex]Cr_{2}O_{3}[/tex]
Explanation:
The reaction equation for given reaction is as follows.
[tex]Cr_{2}O_{3} + 3H_{2} \rightarrow 2Cr + 3H_{2}O[/tex]
Here, 1 mole of [tex]Cr_{2}O_{3}[/tex] reacts with 3 moles of [tex]H_{2}[/tex].
As mass of chromium (III) oxide is given as 76 g and molar mass of chromium (III) oxide [tex](Cr_{2}O_{3})[/tex] is 152 g/mol.
Number of moles is the mass of substance divided by its molar mass. So, moles of [tex]Cr_{2}O_{3}[/tex] is calculated as follows.
[tex]No. of moles = \frac{mass}{molar mass}\\= \frac{76 g}{152 g/mol}\\= 0.5 mol[/tex]
Now, moles of [tex]H_{2}[/tex].given by 0.5 mol of [tex]Cr_{2}O_{3}[/tex] is calculated as follows.
[tex]0.5 mol Cr_{2}O_{3} \times \frac{3 mol H_{2}}{1 mol Cr_{2}O_{3}}\\= 1.5 mol H_{2}[/tex]
As molar mass of [tex]H_{2}[/tex] is 2.016 g/mol. Therefore, mass of [tex]H_{2}[/tex] is calculated as follows.
[tex]No. of moles = \frac{mass}{molar mass}\\1.5 mol = \frac{mass}{2.016 g/mol}\\mass = 3.024 g[/tex]
Thus, we can conclude that 3.024 g grams of hydrogen are needed to convert 76 grams of chromium(III) oxide, [tex]Cr_{2}O_{3}[/tex].
