# Question 5962c

Aug 14, 2016

You need 8.40 g of $\text{Fe}$.

#### Explanation:

Step 1. Use the Ideal Gas Law to calculate the moles of hydrogen.

The Ideal Gas Law is

color(blue)(|bar(ul(PV = nRT)|),

where

• $P$ is the pressure
• $V$ is the volume
• $n$ is the number of moles
• $R$ is the gas constant
• $T$ is the temperature

We can rearrange the Ideal Gas Law to get

$n = \frac{P V}{R T}$

P = 750 color(red)(cancel(color(black)("mmHg"))) × "1 atm"/(760 color(red)(cancel(color(black)("mmHg")))) = "0.9868 atm"
$V = \text{31.0L}$
$R = \text{0.082 06 L·atm·K"^"-1""mol"^"-1}$
$T = \text{(23 + 273.15) K" = "296.15 K}$

n = (PV)/(RT) = (0.9868 color(red)(cancel(color(black)("atm"))) × 31.0 color(red)(cancel(color(black)("L"))))/( "0.082 06" color(red)(cancel(color(black)("L·atm·K"^"-1"))) "mol"^"-1" × 296.15 color(red)(cancel(color(black)("K")))) = "1.259 mol"#

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

The balanced equation is:

$\text{Fe" + "2HCl" → "FeCl"_2 + "H"_2}$

$\text{Moles of Fe" = 1.259 cancel("mol H"_2) × ("1 mol Fe")/(1 cancel("mol H"_2)) = "1.259 mol Fe}$

Step 3. Calculate the mass of $\text{Fe}$

$\text{Mass of Fe" = 1.259 color(red)(cancel(color(black)("mol Fe"))) × ("55.84 g Fe")/(1 color(red)(cancel(color(black)("mol Fe")))) = "70.3 g Fe}$