# What is the volume of #H_2# generated by reacting 4.33g of #Zn# with excess #H_2SO_4# at 38°C and 760 torr?

##### 2 Answers

#### Explanation:

Zinc metal will react with **dilute** *sulfuric acid* to produce *zinc sulfate*, *hydrogen gas*,

The balanced chemical equation for this single replacement reaction looks like this

#"Zn"_text((s]) + "H"_2"SO"_text(4(aq]) -> "ZnSO"_text(4(aq]) + "H"_text(2(g]) uarr#

Notice that you have a **always** produce the same number of moles of hydrogen gas as you have moles of zinc metal that *take part in the reaction*.

In your case, you know that the sulfuric acid is *in excess*, which means that zinc metal acts as a limiting reagent, i.e. it will be **completely consumed** by the reaction.

Use zinc metal's **molar mass** to determine how many moles you have in that

#4.33 color(red)(cancel(color(black)("g"))) * "1 mole Zn"/(65.38color(red)(cancel(color(black)("g")))) = "0.06623 moles Zn"#

This means that the reaction produced

Now, in order to determine the *volume* this much hydrogen gas occupies under those conditions for pressure and temperature, you must use the ideal gas law equation, which looks like this

#color(blue)(PV = nRT)" "# , where

**always** expressed in *Kelvin*!

It's important to notice here that the units given to you for pressure and temperature *do not* match those used in the expression of the universal gas constant.

This means that you have to **convert** these units from *torr* to *atm*, and from *degrees Celsius* to *Kelvin*, respectively.

So, rearrange the ideal gas law equation to solve for

#V = (nRT)/P#

#V = (0.06623 color(red)(cancel(color(black)("moles"))) * 0.0821(color(red)(cancel(color(black)("atm"))) * "L")/(color(red)(cancel(color(black)("moles"))) * color(red)(cancel(color(black)("K")))) * (273.15 + 38)color(red)(cancel(color(black)("K"))))/(760/760color(red)(cancel(color(black)("atm"))))#

#V = "1.692 L"#

Rounded to two sig figs, the number of sig figs you have for the pressure and temperature of the gas, the answer will be

#V = color(green)("1.7 L")#

#### Explanation:

## State the Equation

Zinc's only common oxidation state is

## Calculating Moles of #"H"_2#

First, calculate the **moles** of

Next, calculate the moles of **mole ratio**:

## Calculating Volume of #"H"_2#

In order to find the volume of space occupied by the calculated number of moles of hydrogen gas at the stated conditions, we must consult the **ideal gas equation**:

Where:

#"p"# is**pressure**in**pascals**(#"Pa"# )#"V"# is**volume**in**cubic metres**(#"m"^3# )#"n"# is the**number of moles**#"R"# is the**gas constant**=#8.314# #"T"# is the**temperature**in**Kelvin**(#"K"# )

First, convert the given data into workable units:

#1"torr" ~~ 133.322"Pa", :. 760"torr" = 101325"Pa"# #1^@"C" = 274.15"K", :. 38^@"C" = 311.15"K"#

Next, rearrange the equation to solve for **volume**:

Finally, substitute in your values and solve the equation:

Another useful unit that is probably suitable to use in this situation is the **cubic decimetre** (