Physics, asked by soumyaranjankh13, 1 month ago

An agitated vessel 6 f t(1.83 m) in diameter contains a six blade

straight blade turbine 2 f t(0.61 m) in diameter, set one impeller

diameter above the vessel floor, and rotating at 80 r/min. It is

proposed to use this vessel for neutralizing a dilute aqueous solution

of N aOH at 70oF with a stoichiometrically equivalent quantity of

concentrated nitric acid (HNO3

). The final depth of liquid in the

vessel is to be 6 f t(1.83 m). Assuming that all the acid is added to

the vessel at one time, how long will it take for the neutralization to

be complete?

Answers

Answered by Afreenakbar

Answer:

The mixing time required for complete neutralization is approximately 1.86 seconds.

Explanation:

We must calculate the mixing time necessary for the acid and NaOH to completely react in order to determine the amount of time needed for the neutralisation to be complete.

The following equation can be used to estimate the mixing time:

$tm = 0.04 ( \frac{H}{V})^{0.67} ( \frac{ D}{ \Delta \rho })^{0.33}$

where:

tm = mixing time (in seconds)

H = liquid depth in the vessel (in meters)

V = liquid volume in the vessel (in cubic meters)

D = impeller diameter (in meters)

Δρ = density difference between the two fluids (in kg/m³)

Calculating the volume of liquid in the vessel is the first step.

Given that the vessel has a 6 foot diameter and a 6 foot final liquid depth, the capacity can be computed as follows:

$V = \frac{ \pi }{4 } \times (6 ft)^2 \times (6 ft) \times (0.0283 m/ft)^3$

= 7.74 m³.

The density difference between the NaOH solution and the HNO₃ solution must then be determined. Given that the concentrated HNO₃ solution has a density of 1500 kg/m³, while the NaOH solution is diluted and has a density of 1000 kg/m³, the density difference can be calculated as follows:

$\Delta \rho = 1500 kg/m^3 - 1000 kg/m^3$