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A weak base will have a higher H + concentration than a stronger base because it is less completely protonated than a stronger base and, therefore, more hydrogen ions remain in its solution. Given its greater H + concentration, the formula yields a lower pH value for the weak base.
In mathematics, a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives may not all exist but which is nonetheless deemed to satisfy the equation in some precisely defined sense. There are many different definitions of weak solution, appropriate for different ...
For example, acetic acid is a weak acid which has a = 1.75 x 10 −5. Its conjugate base is the acetate ion with K b = 10 −14 /K a = 5.7 x 10 −10 (from the relationship K a × K b = 10 −14), which certainly does not correspond to a strong base. The conjugate of a weak acid is often a weak base and vice versa.
Weak bases, such as baking soda or egg white, should be used to neutralize any acid spills. Neutralizing acid spills with strong bases, such as sodium hydroxide or potassium hydroxide , can cause a violent exothermic reaction, and the base itself can cause just as much damage as the original acid spill.
However, for weak acids, a quadratic equation must be solved, and for weak bases, a cubic equation is required. In general, a set of non-linear simultaneous equations must be solved. Water itself is a weak acid and a weak base, so its dissociation must be taken into account at high pH and low solute concentration (see Amphoterism).
Hydrogen cyanide is a weak acid in aqueous solution with a pK a of about 9. In strongly alkaline solutions, above pH 11, say, it follows that sodium cyanide is "fully dissociated" so the hazard due to the hydrogen cyanide gas is much reduced. An acidic solution, on the other hand, is very hazardous because all the cyanide is in its acid form.
A weak solution consists of a probability space and a process that satisfies the integral equation, while a strong solution is a process that satisfies the equation and is defined on a given probability space. The Yamada–Watanabe theorem makes a connection between the two. An important example is the equation for geometric Brownian motion
In a weak formulation, equations or conditions are no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain "test vectors" or "test functions". In a strong formulation, the solution space is constructed such that these equations or conditions are already fulfilled.