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Question
The drain cleaner, Drainex contains small bits of aluminum which react with caustic soda to produce dihydrogen. What volume of dihydrogen at 20 °C and one bar will be released when 0.15g of aluminum reacts?
Solution
The chemical equation for the reaction is
\[\ce{\underset{\ce{2 x 27 g}}{2 Al} + 2 NaOH + 2H2O -> 2NaAlO2 + \underset{\ce{3 x 22400 mL}}{3H2}}\]
At STP (273.15 K and 1 atm), 54 g (2 × 27 g) of Al gives 3 × 22400 mL of H2..
∴ 0.15 g Al gives `(3xx22400xx0.15)/54`mL of H2 i.e., 186.67 mL of H2.
= 186.7 mL
S.T.P condition `"V"_1` = 186.7 mL , `"V"_2 = ?`
`"P"_1` = 1.013 bar , `"P"_2` = 1 bar
`"T"_1` = 0 + 273 = 273 K, `"T"_2` = 20 + 273 = 293 K
Accourding to gas equation
`("P"_1"V"_1)/"T"_1 = ("P"_2"V"_2)/"T"_2` or
`"V"_2 = ("P"_1"V"_1"T"_2)/("P"_2"T"_1)`
`"V"_2 = (1.013 " bar" xx 186.7 " mL" xx 293" K")/ (1 "bar" xx 273 " K")`
= 203 mL
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