Question

If an aqueous solution of HNO3 is electrolyzed for 13.00 min at a steady current of 1.45 A, what volume of H2 (g) at 25.0oC and 1.03 atm will be collected at the cathode? vol H2 (L)

Answer 1

Answer: 0.14 Liters

Explanation:

$Q=I\times t$

where Q= quantity of electricity in coloumbs

I = current in amperes = 1.45 A

t= time in seconds = 13 min=$13\times 60 =780s$

$Q=1.45A\times 780s=1131C$

$HNO_3\rightarrow H^++NO_3^-$

$2H^++2e^-\rightarrow H_2$

$96500\times 2=193000Coloumb$ of electricity deposits  1 mole of $H_2$

1131 C of electricity deposits =$\frac{1}{193000}\times 1131=5.86\times 10^{-3}moles$ of $H_2$

According to the ideal gas equation:'

$PV=nRT$

P = Pressure of the gas = 1.03 atm

V= Volume of the gas = ?

T= Temperature of the gas = 25°C = 298 K       (0°C = 273 K)

R= Gas constant = 0.0821 atmL/K mol

n=  moles of gas= $5.86\times 10^{-3}moles$

$V=\frac{nRT}{P}=\frac{5.86\times 10^{-3}\times 0.0821\times 298}{1.03}=0.14L$

Thus the volume of hydrogen gas at $25^0C$ and 1.03 atm will be 0.14 Liters.