Respuesta :
ANSWER
The volume of butane in mL is 5967 mL
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
[tex]\text{ The molecular formula of butane is C}_4H_{10}[/tex]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
[tex]\begin{gathered} \text{ The molar mass of C}_4H_{10}\text{ = \lparen4}\times12)\text{ + \lparen1}\times10) \\ \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}[/tex]Step 3: Find the mole of butane using the below formula
[tex]\text{ Mole = }\frac{\text{ mass}}{\text{ molar mass}}[/tex]Recall, that the mass of butane is 15.45 grams as provided in the question
[tex]\begin{gathered} \text{ Mole = }\frac{15.45}{58} \\ \text{ Mole = 0.2664 mol} \end{gathered}[/tex]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
[tex]\begin{gathered} \text{ 1 mole }\rightarrow\text{ 22.4L} \\ 0.2664\rightarrow\text{ xL} \\ \text{ cross multiply} \\ \text{ 1 mole}\times xL\text{ = 0.2264 mole}\times22.4L \\ \text{ Isolate x} \\ \text{ xL = }\frac{0.2264\cancel{mole}\times22.4L}{1\cancel{mole}} \\ \text{ x = 5.967 L} \\ \text{ x = 5967 mL} \end{gathered}[/tex]Hence, the volume of butane in mL is 5967 mL
