# Question #ec36a

Aug 14, 2017

(a) 5.00 mol; (b) 50.0 u; (c) 10.0 g; (d) 25.0 g.

#### Explanation:

(a) Mass of $\text{A"_2"B}$

Your equation is not in its lowest terms. It should be

${M}_{\textrm{r}} : \textcolor{w h i t e}{m} 40.0 \textcolor{w h i t e}{m l} 30.0 \textcolor{w h i t e}{m m l} 50.0$
$\textcolor{w h i t e}{m m m l l} \text{A"_2 + "2AB" → "2A"_2"B}$

Step 2. Calculate the moles of $\text{A"_2"B}$.

$\text{Moles of A"_2"B" = 2.50 color(red)(cancel(color(black)("mol A"_2))) × ("2 mol A"_2"B")/(1 color(red)(cancel(color(black)("mol A"_2)))) = "5.00 mol A"_2"B}$

(b) Molecular mass of $\text{A"_2"B}$

If $\text{Molec. mass of A"_2 = "40.0 u}$, then $\text{at. mass of A" = "20.0 u}$

$\text{Molec. mass of AB" = "30.0 u" = "20.0 u + at. mass of B}$

$\text{At. mass of B" = "30.0 u - 20.0 u" = "10.0 u}$

$\text{Molec. mass of A"_2"B" = "2 × 20.0 u + 10.0 u" = "40.0 u + 10.0 u" = "50.0 u}$

(c) Mass of ${\text{A}}_{2}$ required

Step 1. Calculate the moles of $\text{AB}$

$\text{Moles of AB" = 15.0 color(red)(cancel(color(black)("g AB"))) × (1 "mol AB")/(30.0color(red)(cancel(color(black)("g AB")))) = "0.500 mol AB}$

Step 2. Calculate the moles of of ${\text{A}}_{2}$

${\text{Moles of A"_2 = 0.500 color(red)(cancel(color(black)("mol AB"))) × "1 mol A"_2/(2 color(red)(cancel(color(black)("mol AB")))) = "0.250 mol A}}_{2}$

Step 3. Calculate the mass of ${\text{A}}_{2}$

${\text{Mass of A"_2 = 0.250 color(red)(cancel(color(black)("mol A"_2))) × "40.0 g A"_2/(1 color(red)(cancel(color(black)("mol A"_2)))) = "10.0 g A}}_{2}$

(d) Mass of $\text{A"_2"B}$ formed

Step 1. Calculate the moles of $\text{A"_2"B}$ formed

$\text{Moles of A"_2"B" = 0.500 color(red)(cancel(color(black)("mol AB"))) × ("2 mol A"_2"B")/(2 color(red)(cancel(color(black)("mol AB")))) = "0.500 mol A"_2"B}$

Step 2. Calculate the mass of $\text{A"_2"B}$

$\text{Mass of A"_2"B" = 0.500 color(red)(cancel(color(black)("mol A"_2"B"))) × ("50.0 g A"_2"B")/(1 color(red)(cancel(color(black)("mol A"_2"B")))) = "25.0 g A"_2"B}$