Question

If 38.5 grams of lithium metal reacts with excess water, how many liters of hydrogen gas are produced at STP? 2Li + 2H2O → 2LiOH + H2

Answer 1

The volume of hydrogen gas is 62.16L

Step-by-step explanation

Given information

The mass of lithium metal = 38.5 grams

The first step is to write a balanced chemical reaction equation for the reaction

`2Li_((s))+2H_2O_(l))\text{ }\rightarrow2LiOH_((aq))+H_(2(g))`

From the above reaction, you can see that 2 moles of lithium metal react with 2 moles of water to give 2 moles of lithium hydroxide and 1 mole of hydrogen gas

The next step is to find the mole of lithium metal using the below formula

`\text{mole = }\frac{\text{ reacting mass}}{\text{ molar mass}}`

According to the periodic table, the molar mass of lithium metal is 6.941 u

Recall that, the mass of lithium is 38.5 g

Therefore, the mole can be calculated as

`\begin{gathered} \text{mole = }\frac{\text{ 38.5}}{6.941} \\ \text{mole = 5.55 moles} \end{gathered}`

From the above calculation, you will see that the mole of lithium metal is 5.55 moles

The next step is to find the mole of hydrogen gas using a stoichiometry ratio

From the reaction above, you will see that 2 moles of lithium metal give 1 mole of hydrogen gas

Let x represents the number of moles of hydrogen gas

`\begin{gathered} 2\text{ moles of Li }\rightarrow1moleofH_2 \\ 5.55\text{ moles of Li }\rightarrow xmoleofH_2 \\ \text{Mathematically,} \\ 2\text{ = 1} \\ 5.55\text{ = x} \\ \text{cross multiply} \\ 2\cdot\text{ x = 1 }\cdot\text{ 5.55} \\ 2x\text{ = 5.55} \\ \text{Divide both sides by 2} \\ (2x)/(2)\text{ = }(5.55)/(2) \\ x\text{ = 2.775 moles} \end{gathered}`

Therefore, the number of moles of hydrogen gas is 2.775 moles

The next step is to find the volume of hydrogen gas from the calculated number of moles

Recall that at STP, 1 mole is equivalent to 22.4 L

Let x represents the volume of the hydrogen gas

`\begin{gathered} 1\text{ mole }\rightarrow\text{ 22.4L} \\ 2.775\text{ moles }\rightarrow\text{ xL} \\ \text{Cross multiply} \\ \text{ 1 }\cdot\text{ x = 22.4 }*\text{ 2.775} \\ x\text{ = 62.16L} \end{gathered}`

Therefore, the volume of hydrogen gas is 62.16L