Respuesta :
Answer:
1,7Kg of [tex]H_{2} O[/tex] is produced
Explanation:
Balanced chemical reaction
To find the mass of [tex]H_{2} O[/tex] produced in a reaction, we need to start by identifying that chemical reaction and balancing it.
The question give us the reactants and the products, do we know:
[tex]C_{57}H_{110}O_{6}[/tex] + [tex]O_{2}[/tex] ⇒[tex]CO_{2}[/tex] + [tex]H_{2} O[/tex]
Counting C, H and O in reactants and products; and balancing them with stoichiometric coefficients, we have that the balanced chemical equation is:
2 [tex]C_{57}H_{110}O_{6}[/tex] + 160 [tex]O_{2}[/tex] ⇒ 114[tex]CO_{2}[/tex] + 110 [tex]H_{2} O[/tex]
Stoichiometry
The question says us that 1.2 Kg of fat ([tex]C_{57}H_{110}O_{6}[/tex]) react.
To find the amount of [tex]H_{2} O[/tex] we need to find the moles of [tex]C_{57}H_{110}O_{6}[/tex]. The way to do it, is using the molar mass:
Taking the molar mass of each element in the periodic table, multiplying by the subscript and adding all the partial values:
[tex](12.0107)*57+(1.00794)*110+(15.9994)*6= 891.48 \frac{g}{mol}[/tex]
The moles of [tex]C_{57}H_{110}O_{6}[/tex] that react are:
[tex]1.2 Kg *\frac{1000g}{1Kg} * \frac{1 mol }{ 891.48 g}[/tex] [tex]= 1.6826 mol[/tex] [tex]C_{57}H_{110}O_{6}[/tex]
The balanced chemical reaction tell us that each 2 moles of [tex]C_{57}H_{110}O_{6}[/tex] that react, produce 110 moles of [tex]H_{2} O[/tex]. It means that:
1.6826 mol [tex]C_{57}H_{110}O_{6}[/tex] [tex]* \frac{110 mol H_{2}O}{2 mol C_{57}H_{110}O_{6}}[/tex][tex]=92.543[/tex] mol [tex]H_{2} O[/tex]
Finally, using the molar mass of [tex]H_{2} O[/tex], we can find its mass:
92.543 mol [tex]H_{2} O[/tex][tex]*\frac{18 g}{1 mol}[/tex] =1665.7 g
With two sig figs, the mass:
1665.7g[tex]*\frac{1 Kg}{1000g}[/tex] ≅ 1.7 Kg
