Questions: Solve the following multi-step mole conversion problem: 0.192 kilograms of SO2 is equal to how many liters of SO2 at STP? *Record your answer to three significant digits and include leading zeros ( 0.5 , not .5 )

Solution Steps

First, we need to convert the mass of \(\mathrm{SO}_2\) from kilograms to grams, since the molar mass is typically given in grams per mole.

\[ 0.192 \, \text{kg} = 192 \, \text{g} \]

Next, we use the molar mass of \(\mathrm{SO}_2\) to convert grams to moles. The molar mass of \(\mathrm{SO}_2\) is calculated as follows:

• Sulfur (S): \(32.06 \, \text{g/mol}\)
• Oxygen (O): \(16.00 \, \text{g/mol} \times 2 = 32.00 \, \text{g/mol}\)

Thus, the molar mass of \(\mathrm{SO}_2\) is:

\[ 32.06 \, \text{g/mol} + 32.00 \, \text{g/mol} = 64.06 \, \text{g/mol} \]

Now, convert grams to moles:

\[ \text{Moles of } \mathrm{SO}_2 = \frac{192 \, \text{g}}{64.06 \, \text{g/mol}} = 2.9969 \, \text{mol} \]

At standard temperature and pressure (STP), 1 mole of any ideal gas occupies 22.414 liters. Therefore, we can convert moles to liters:

\[ \text{Liters of } \mathrm{SO}_2 = 2.9969 \, \text{mol} \times 22.414 \, \text{L/mol} = 67.168 \, \text{L} \]

Final Answer