Sure, let's walk through the solution step by step:
1. Convert the temperature from Celsius to Kelvin:
[tex]\[
T(K) = T(°C) + 273.15
\][/tex]
Given [tex]\( T(°C) = 75.31 \)[/tex]:
[tex]\[
T(K) = 75.31 + 273.15 = 348.46 \, \text{K}
\][/tex]
2. Calculate the number of moles of [tex]\( Cu_2S \)[/tex] (Copper(I) sulfide):
-
We know the mass of [tex]\( Cu_2S \)[/tex] is 14.29 grams.
-
The molar mass of [tex]\( Cu_2S \)[/tex] can be calculated as:
[tex]\[
\text{Molar mass of } Cu_2S = 2 \times 63.55 \, (\text{atomic mass of Cu}) + 32.06 \, (\text{atomic mass of S}) = 159.16 \, \text{g/mol}
\][/tex]
-
The number of moles is then:
[tex]\[
\text{Moles of } Cu_2S = \frac{\text{mass}}{\text{molar mass}} = \frac{14.29 \, \text{g}}{159.16 \, \text{g/mol}} \approx 0.08978 \, \text{moles}
\][/tex]
3. Determine the moles of [tex]\( SO_2 \)[/tex] produced:
From the balanced chemical equation:
[tex]\[
Cu_2S (s) + O_2 (g) \rightarrow Cu_2O (s) + SO_2 (g)
\][/tex]
We see that 1 mole of [tex]\( Cu_2S \)[/tex] produces 1 mole of [tex]\( SO_2 \)[/tex]. Therefore:
[tex]\[
\text{Moles of } SO_2 \text{ produced} = \text{Moles of } Cu_2S \approx 0.08978 \, \text{moles}
\][/tex]
4. Calculate the volume of [tex]\( SO_2 \)[/tex] gas produced using the Ideal Gas Law:
The Ideal Gas Law is given by:
[tex]\[
PV = nRT \implies V = \frac{nRT}{P}
\][/tex]
Where:
-
[tex]\( n \)[/tex] = number of moles of [tex]\( SO_2 \)[/tex] = 0.08978 moles,
-
[tex]\( R \)[/tex] = Ideal Gas Constant = 0.0821 atm·L/(mol·K),
-
[tex]\( T \)[/tex] = temperature in Kelvin = 348.46 K,
-
[tex]\( P \)[/tex] = pressure in atm = 0.851 atm.
-
Then:
[tex]\[
V = \frac{0.08978 \, \text{moles} \times 0.0821 \, \text{atm·L/(mol·K)} \times 348.46 \, \text{K}}{0.851 \, \text{atm}} \approx 3.018 \, \text{L}
\][/tex]
Therefore, the volume of sulfur dioxide ([tex]\( SO_2 \)[/tex]) gas produced is approximately [tex]\( 3.018 \, \text{L} \)[/tex].
