Respuesta :
Answer: The volume of hydrogen sulfide gas is 38.8 L.
Explanation:
The given reaction equation is as follows.
[tex]Al_{2}S_{3}(s) + 6H_{2}O(l) \rightarrow 3H_{2}S(g) + 2Al(OH)_{3}(aq)[/tex]
Mass of [tex]Al_{2}S_{3}[/tex] is given as 65.0 g. Hence, moles of [tex]Al_{2}S_{3}[/tex] (molar mass = 150.158 g/mol) is calculated as follows.
[tex]Moles = \frac{mass}{molar mass}\\= \frac{65.0 g}{150.158 g/mol}\\= 0.433 mol[/tex]
As 1 moles of [tex]Al_{2}S_{3}[/tex] is giving 3 moles of [tex]H_{2}S[/tex]. Hence, moles of [tex]H_{2}S[/tex] formed by 0.433 moles of [tex]Al_{2}S_{3}[/tex] are as follows.
[tex]Moles of H_{2}S = 0.433 mol \times \frac{3 mol H_{2}S}{1 mol Al_{2}S_{3}}\\= 1.299 mol[/tex]
Here, pressure is 0.987 atm and temperature is [tex](90 + 273) K = 368 K[/tex]. Therefore, volume of hydrogen sulfide is calculated as follows.
PV = nRT
where,
P = pressure
V = volume
n = no. of moles
R = gas constant = 0.0821 L atm/mol K
T = temperature
Substitute the values into above formula as follows.
[tex]PV = nRT\\0.987 atm \times V = 1.299 mol \times 0.0821 L atm/mol K \times 368 K\\V = 38.8 L[/tex]
Thus, we can conclude that volume of hydrogen sulfide gas is 38.8 L.
