To determine the mass of [tex]\( O_2 \)[/tex] required to completely react with [tex]\( 0.025 \, \text{g} \, C_3H_8 \)[/tex], we can follow a step-by-step approach that involves calculating the moles of propane, finding the stoichiometric moles of oxygen needed, and then converting that to mass.
1. Calculate the moles of [tex]\( C_3H_8 \)[/tex]:
The molar mass of [tex]\( C_3H_8 \)[/tex] is [tex]\( 44.1 \, \text{g/mol} \)[/tex]. Given the mass of [tex]\( C_3H_8 \)[/tex] is [tex]\( 0.025 \, \text{g} \)[/tex], we compute the moles of [tex]\( C_3H_8 \)[/tex] as follows:
[tex]\[
\text{moles of } C_3H_8 = \frac{0.025 \, \text{g}}{44.1 \, \text{g/mol}} = 0.0005668934240362812 \, \text{mol}
\][/tex]
2. Determine the moles of [tex]\( O_2 \)[/tex] required:
According to the balanced chemical equation:
[tex]\[
C_3H_8 + 5 O_2 \rightarrow 3 CO_2 + 4 H_2O
\][/tex]
1 mole of [tex]\( C_3H_8 \)[/tex] reacts with 5 moles of [tex]\( O_2 \)[/tex]. Therefore, the moles of [tex]\( O_2 \)[/tex] required are:
[tex]\[
\text{moles of } O_2 = 0.0005668934240362812 \, \text{mol} \times 5 = 0.002834467120181406 \, \text{mol}
\][/tex]
3. Calculate the mass of [tex]\( O_2 \)[/tex]:
The molar mass of [tex]\( O_2 \)[/tex] is [tex]\( 32.00 \, \text{g/mol} \)[/tex]. Therefore, the mass of [tex]\( O_2 \)[/tex] required can be determined as:
[tex]\[
\text{mass of } O_2 = 0.002834467120181406 \, \text{mol} \times 32.00 \, \text{g/mol} = 0.09070294784580499 \, \text{g}
\][/tex]
Thus, the mass of [tex]\( O_2 \)[/tex] required to completely react with [tex]\( 0.025 \, \text{g} \, C_3H_8 \)[/tex] is [tex]\( 0.091 \, \text{g} \)[/tex]. Hence, the correct answer is [tex]\( 0.091 \, \text{g} \)[/tex].
