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A typical titration curve of a diprotic acid, oxalic acid, titrated with a strong base, sodium hydroxide.Both equivalence points are visible. Titrations are often recorded on graphs called titration curves, which generally contain the volume of the titrant as the independent variable and the pH of the solution as the dependent variable (because it changes depending on the composition of the ...
The McCabe–Thiele method is a technique that is commonly employed in the field of chemical engineering to model the separation of two substances by a distillation column. [1] [2] [3] It uses the fact that the composition at each theoretical tray is completely determined by the mole fraction of one of the two components.
Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
Figure 2 gives an example; in this example, the two x-intercepts differ by about 0.2 mL but this is a small discrepancy, given the large equivalence volume (0.5% error). Similar equations can be written for the titration of a weak base by strong acid (Gran, 1952; Harris, 1998).
Given the two red points, the blue line is the linear interpolant between the points, and the value y at x may be found by linear interpolation. In mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.
This means that you can no longer pick any two arbitrary points and compute the slope. Instead, the slope of the graph can be computed by considering the tangent line—a line that 'just touches' a particular point. [a] The slope of a curve at a particular point is equal to the slope of the tangent to that point. For example, = has a slope of ...
The coefficient is calculated by taking the shifted median of all slopes of the straight lines between any two points, disregarding lines for which the points are identical or =. The median is shifted based on the number of slopes where b < − 1 {\displaystyle b<-1} to create an approximately consistent estimator.
the slope field is an array of slope marks in the phase space (in any number of dimensions depending on the number of relevant variables; for example, two in the case of a first-order linear ODE, as seen to the right). Each slope mark is centered at a point (,,, …,) and is parallel to the vector