Question

A butane lighter contains 15.45 grams of butane at STP. How many milliliters is this?

Answer 1

The volume of butane in mL is 5967 mL

Step-by-step explanation

Given that;

The mass of butane is 15.45 grams

Follow the steps below to find the volume of butane in mL

Step 1: Write the molecular formula of butane

`\text{ The molecular formula of butane is C}_4H_(10)`

Step 2: Find the molar mass of butane

In the above molecular formula, butane has 4 carbon atoms and 10 hydrogen atoms

Recall, that the mass unit of carbon is 12u and the mass unit of hydrogen is 1.0u

`\begin{gathered} \text{ The molar mass of C}_4H_(10)\text{ = \lparen4}*12)\text{ + \lparen1}*10) \\ \text{ The molar mass of C}_4H_(10)\text{ = 48 + 10} \\ \text{ The molar mass of C}_4H_(10)\text{ = 58 g/mol} \end{gathered}`

Step 3: Find the mole of butane using the below formula

`\text{ Mole = }\frac{\text{ mass}}{\text{ molar mass}}`

Recall, that the mass of butane is 15.45 grams as provided in the question

`\begin{gathered} \text{ Mole = }(15.45)/(58) \\ \text{ Mole = 0.2664 mol} \end{gathered}`

Step 4: Find the volume of butane in mL

Recall, that 1 mole of a gas is equivalent to 22.4L molar volume

Let x represents the volume of butane

From the above data in step 4, we can now find the volume of butane

`\begin{gathered} \text{ 1 mole }\rightarrow\text{ 22.4L} \\ 0.2664\rightarrow\text{ xL} \\ \text{ cross multiply} \\ \text{ 1 mole}* xL\text{ = 0.2264 mole}*22.4L \\ \text{ Isolate x} \\ \text{ xL = }\frac{0.2264\cancel{mole}*22.4L}{1\cancel{mole}} \\ \text{ x = 5.967 L} \\ \text{ x = 5967 mL} \end{gathered}`

Hence, the volume of butane in mL is 5967 mL