Mass Flow Rate

Normally flow rates are given in a molar basis. However, in this case it is easier to use a mass flow rate because referring to a hippo’s feed rate in terms of moles is impractical. The justification for the substitution of molar for mass flow rate follows:

dF_A=r_A*dV

where F_A is the molar flow rate of A in Moles of A per unit time(e.g. mol/s). r_A is the rate of formation in Moles of A formed per unit time per unit volume (e.g. mol/dm³/s).

Multiplying by the molecular weight of A:

M_WA*dF_A=d(M_WA*F_A)=(r_A*M_WA)*dV

then

dm_A=r_MA*dV

where

m_A is the mass flow rate of A in mass flow rate of A, mass per unit time.(e.g., kg/s)

r_MA is the mass rate of formation of A, mass of A per unit time per unit volume (e.g., kg/dm³/s).

thus,

X= moles of A reacted per mole of a feed = mass of A reacted per mass or A fed.

Proof

X=1-F_A/F_AO

Multiply numerator and denominator by the molecular weight of A

X=1-F_A/F_AO=1-M_WA*F_A/(F_AO*M_WA)=1-m_A/m_AO