Plot of concentration vs. time

The mass transfer coefficient in liquid membrane, k , can be obtained from the plot of concentration vs. time. 

For a zeroth-order reaction, a plot of concentration vs time gives a straight line with slope = — k. (The units of k here are mol L 1 s 1). 

Often a plot of concentration vs. time, or the monitored parameter vs. time, or the rate plot, will not be monophasic. This can arise from a number of different situations, the more common of which are described below. 

Equations tl8-79) and ri8-80al can be used to analyze experimental peaks, which are essentially plots of concentration vs. time, to determine the value of u and N. From Eq. tl8-791 the peak maximum must... 

We determine an initial rate from a plot of concentration vs. time, so we need a quick, accurate method for measuring concentration. Let s briefly discuss three common approaches. 

Series of plots of concentration vs. time Determine slope of tangent at to for each plot. Initial rates A Compare initial rates when [A] (Ganges and B] is held Reaction orders Substitute initial rates, orders, and concentrations into rate = Rate constant (k)and actual rate law... 

The integration of Eqs. 11.3-9 to 11.3-11 is straightforward but complicated. It leads to a plot of concentration vs. time which is a weighted sum of two decaying exponentials. To understand what this means, we are better off to consider a couple of special cases. 

The result of the first experiment is a breakthrough curve, a plot of concentration vs. time like that shown in Fig. 15.3-4. We can learn a lot about the adsorption from the shape of this curve. The total amount fed to the bed from time zero to time t is of... 

Report the concentrations of A and C cells and plot [A] and [C] versus iterations, n. Is the initial rate (slope of a plot of [C] vs. time) changed ... 

The decomposition data forjNO plotted as the reciprocal of concentration vs. time. This graph is linear, with a slope equal to the second-order rate constant. 

Fig. 1.1 The characteristics of (a) zero- (b) first- and (c) second-order reactions. In (a) the concentration of A decreases linearly with time until it is all consumed at time T. The value of the zero-order rate constant is given by Aq/T. In (b) the loss of A is exponential with time. The plot of In [A], vs time is linear, the slope of which is k, the first-order rate constant. It obviously does not matter at which point on curve (b) the first reading is taken. In (c) the loss of A is hyperbolic with time. The plot of [A], vs time is linear with a slope equal to k, the second-order rate constant.

Chemical test using sulphur as an hydrogen acceptor Sulphur will readily accept donatable hydrogen to produce H2S whose partial pressure will be proportional to the concentration of H-donors. This reaction provides a simple method for monitoring H-donors contents and initial experiments showed that only small amounts of sulphur and the hydrogen donor compound were needed for the reaction. The method was calibrated using 0.5 g of sulphur with various amounts of 9,10 dihydrophenanthrene (H2) which were reacted at 275 C in a 10 cm3 microautoclave. Plots of pressure vs. time (Figure 3) indicates that an equilibrium pressure was reached in 30 mins or less. 

In order to find the initiation rate, a set of polymerizations, in the presence of inhibitor (2,2,6,6-tetramethyl-4-hydroxy-piperidine-l-oxy), was carried out. Inhibition period was measured for polymerization with poly(dimethylmethacrylate), polyethylene glycol, or without any template. The results are presented on the Figure 8.10. The plot of concentration vs. inhibition time is a straight line — the same for all experimental points. It means that initiation rate is the same, independent of the presence of tern-... 

The pH, temperature, substrate concentration, and storage time of the standard reaction test related to both forms of invertase were changed one by one at the intervals cited above. In each case, the activity corresponded to the slope of the straight line attained through a plot of TRS vs time. 

Treatment of Data. Chemical measurement data in each irradiation chamber experiment are plotted as concentration vs. time, and the rates and dosages are determined from the points and best-fit experimental curves. The name of the compound and initial chamber concentrations are entered on computer cards along with the following observations ... 

The effect of concentration is seen in Figure 6. It is but typical of all such plots of t vs. time, constant Z and temperature, with [Hf]ToT as the parameter. This result is the only one to emerge from this study which is unexpected. 

Tier 1 - Extrapolation Source zones that have extended records of concentration vs. time can be analyzed using the Tier 1 extrapolation tool. With this tool, log concentration vs. time is plotted and then extrapolated to estimate how long it will take to achieve a cleanup goal, assuming the current trend continues. This tool also provides the 90% and 95% confidence level in this estimate of the time to achieve the cleanup goal. 

Figure 16.7 A plot of [N2O5] vs. time for three half-lives. During each half-life, the concentration is halved (7 = 45°C and [N205]o = 0.0600 mol/L). The blow-up volumes, with N2O5 molecules as colored spheres, show that after three half-lives,...

Figure 1 shows the standard, first-order kinetics plots of the data natural logarithm of concentration vs. time. The rate of loss based on estimated sunlight is faster than that for actual time, but the difference loses significance at the 95% confidence level. 

The most natural, and most common, method to look at and present one s data is the way in which those data are taken. In a typical experiment, we measure some function of concentration (e.g., electrode potential or absorbance) as a function of time at one set of constraints. A plot of signal vs. time is known as a time series. Time series can be exceedingly dull, for example, in the case of a steady state, or they can be quite difficult to interpret, as in the case of a system that may or may not be chaotic. Nevertheless, they can yield valuable information, and they are certainly the first thing one should look at before proceeding further. Figure 2.12 shows a time series that establishes the occurrence of bistability in the arsenite-iodate reaction. 

The potential (E) of a working electrode measured in the methanol-receiving compartment has an inverse relationship with the methanol concentration. As such, the potential (E) values obtained with time can be used to determine the methanol concentrations (CJf)) as a function of time. Plot of CJit)) vs. time will give... 

---