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?

Asked by Pragya Singh | 1 year ago |  54

##### Solution :-

The reaction of aluminum with caustic soda is as given below:

2Al + 2NaOH + 2H2O → 2NaAlO2 + 3H2

At Standard Temperature Pressure

(273.15 K and 1 atm), 54 g ( 2 × 27 g)

of Al gives 3 ×22400 mL of H2

Therefore, 0.15 g Al gives:

$$\dfrac{3 \; \times \; 22400 \; \times \; 0.15}{54}mL$$ of H2

= 186.67 mL of H2

At Standard Temperature Pressure,

$$p_{ 1 }$$ = 1 atm

$$V_{ 1 }$$​ = 186.67 mL

$$T_{ 1 }$$= 273.15 K

Let the volume of dihydrogen be

$$V_{ 2 } \;at\; p_{ 2 }$$

$$0.987 \;atm (since\; 1\; bar = 0.987 atm)$$

$$and\; T_{ 2 }= 20^{\circ} C$$

$$= (273.15 + 20) K$$

$$= 293.15 K.$$

Now,

$$\dfrac{p_{ 1 }V_{ 1 }}{T_{ 1 }}= \dfrac{p_{ 2 }V_{ 2 }}{T_{ 2 }}$$

$$V_{ 2 } = \dfrac{p_{ 1 }V_{ 1 }T_{ 2 }}{p_{ 2 }T_{ 1 }}$$

=$$\dfrac{1 \; \times \; 186.67 \; \times \; 293.15}{0.987 \; \times \; 273.15}$$

= 202.98 mL

= 203 mL

Hence, 203 mL of dihydrogen will be released.

Answered by Abhisek | 1 year ago

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