Question #228513

The power needed to drive a certain fan can be computed as follows:

Power(kW)=2.72×10−5QP

Power(kW)=2.72×10−5QP

where Q is the fan volume in m^{3}/h and P is the total discharge pressure in cmH_{2}O.

a. What is the corresponding unit of the formula constant?

b. Transform the formula to compute power in horsepower (hp), using fan volume in ft^{3}/min and pressure in inH_{2}O.

Expert's answer

The rate of a chemical reaction r (or c t^-1) is given by:

r = k [A]^a x [B]^b

where k is the rate constant, A and B are the concentrations of the two reactants and the exponents a and b are integers and give the order of the reaction. The overall kinetic order is the summation of a and b.

If we apply units where c is the concentration in moles or mass per litre, then,

c t^-1 = k x c^a x c^b,

or k = ct^-1/(c^a x c^b)

Therefore the units of the rate constant depend on the kinetic order of the reaction. Assuming the various possibilities of 0, 1, 2 or 3 for the orders will determine the units of k.

For a first order involving one chemical entity, the unit of k is ct^-1/(c^1) or t^-1.

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