9 votes
Accepted

How to (numerically) model a phosphoric acid titration curve

Much easier is to calculate the inverse function $[\ce{Na+}]=f([\ce{H+}],K_\mathrm{a1},K_\mathrm{a2},K_\mathrm{a3})$. Calculate fractions of respective phosphate forms as the function of $\ce{[H+]}$ ...
Poutnik's user avatar
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9 votes

accurate measurement from inaccurate tools

Generally, improvement of measurement process has much better positive impact on results, than sophisticated mathematical processing of low quality data. But, sometimes we are forced to data what we ...
Poutnik's user avatar
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7 votes
Accepted

How to read a chromatography calibration curve?

I assume your teacher explained the HPLC separation. If injected a mixture of four ions you will get four peaks. Each peak has an area, which is proportional to the concentration of the substance. ...
AChem's user avatar
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6 votes
Accepted

Should durations of time be considered to determine final significant figures of answer?

[OP] When calculating sig-figs, do you consider the number of significant-figures for all given values, including durations, or just physical quantities? You consider all physical quantities ...
Karsten's user avatar
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6 votes

accurate measurement from inaccurate tools

Your non-trivial question has a yes and a no. It is not possible to increase the accuracy of a dataset just by mathematical means. If you knew the systematic error in your data then you can do the ...
AChem's user avatar
  • 40.2k
5 votes

what is the issue in evaluating two electron integral?

The main problem of 2-electron integrals is their amount. They are given by \begin{equation} I_{ijkl} = \langle ij|r^{-1}_{12}|kl\rangle \end{equation} where $i$, $j$, $k$ and $l$ run over all $N$...
Feodoran's user avatar
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5 votes

How to read a chromatography calibration curve?

Suppose it is a calibration curve of high performance liquid chromatography (HPLC) to determine concentration of chloride ion in unknown solutions. The detector is sensitive to charge ions, which gave ...
Mathew Mahindaratne's user avatar
5 votes

How should you report measurements and uncertainty for a measuring cylinder with 0.5 mL graduations?

common convention is to report the uncertainty of an analogue instrument as plus or minus half of the smallest scale division Yes, this is merely a poor convention propagated by general chemistry ...
AChem's user avatar
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4 votes

How to (numerically) model a phosphoric acid titration curve

The R code equivalent of Poutnik's answer, for refrence: ...
Naiky's user avatar
  • 133
3 votes
Accepted

The algebraic problem in the equilibrium of weak acids and bases

This sort of derivation is a just painful, but straightforward. As Poutnik mentioned it is just a series of equations where you eliminate variables by substitution. So start with the basics. $\ce{HA &...
MaxW's user avatar
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3 votes

How to read a chromatography calibration curve?

If we take 1st and last points on your graph we'd see that: At concentration $\pu{350ppm}$ your detector shows number $45$ At concentration around $0$ your detector shows number around $0$ So what if ...
Stanislav Bashkyrtsev's user avatar
3 votes

How to read a chromatography calibration curve?

The line goes according to : $y = 0.1312~x$ ; In other words the area of the peak is equal to $0.1312$ times the concentration of chloride in ppm. This result is extremely useful. If for example, in a ...
Maurice's user avatar
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3 votes

the number of significant figures

The significant digits you use are the values of which you are confident, plus one more value which may be uncertain. In this case, the balance is accurate to $\pm0.001$ mg, so you're confident about ...
Spontification's user avatar
3 votes

How to round correctly when calculating the average and standard deviation?

I figured it out. The means are rounded to only two sig figs because its subtraction. And significant figures follow different rules under subtraction/addition vs multiplication/division. And its 0....
eromod's user avatar
  • 305
3 votes

Does the addition or multiplication rule have precedence deciding the significant figures in 5×5.364?

If this is the question in its entirety, then you should not try to 'guess' what the origin, and therefore the accuracy, of the measurement 5 is. You should take it on face value, and complete the ...
long's user avatar
  • 11.9k
2 votes

Does the addition or multiplication rule have precedence deciding the significant figures in 5×5.364?

Using the addition rule doesn't make any sense because then you would always use the addition rule for multiplication. You would use the multiplication rule, and if this question was given as-is, 30 ...
SendersReagent's user avatar
2 votes

How to numerically solve a reaction network with fast equilibrium steps?

For A adsorption: $$r_1=0$$ because the reaction is in equilibrium.So, $$K_1=\frac{[A]}{P_A \times [*]}$$ From this equation you can relate $[A]$ to $[*]$.Similarly, using the last reaction you can ...
Osman Mamun's user avatar
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2 votes
Accepted

Balancing chemical reactions, issues of Gauss's elimination method

Your "should-be" solution, $$\ce{3H2O2 + 2NO3- + 2H+ → 3O2 + 2NO + 4H2O}$$ is a linear combination of $$\ce{H2O2 + 2NO3- + 2H+ → 2O2 + 2NO + 2H2O}$$ and $$\ce{2H2O2 → O2 + 2H2O}$$ Any other ...
Karsten's user avatar
  • 40.2k
2 votes

Factorizing Slater determinant into product of spin-up and spin-down slater determinant

Gopal Iyer's answer is only partially correct and doesn't contain the right interpretation of the citation in the question in my opinion. First I would like to shed some more light on Gopal Iyer's ...
stonar96's user avatar
  • 121
2 votes
Accepted

Factorizing Slater determinant into product of spin-up and spin-down slater determinant

When exchange effects are not taken into consideration, the simplest possible description of a many-body wave function is simply the Hartree product, i.e. the product of individual-particle wave ...
Gopal Iyer's user avatar
2 votes

Calculating the total uncertainty of the final product

General approach \begin{equation} \sigma_{F}^2 = \sum \left( \frac{\partial F}{\partial x_i} \right)^2 \mathrm{d}x_i^2 \end{equation} Here we neglect all correlation terms formed by squaring ...
B. Kelly's user avatar
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2 votes

accurate measurement from inaccurate tools

Experimental design also comes into the fray. If you have an apparatus that is not quantitatively accurate, you can apply it to your experimental ssmple and to a control for ccx which you have a ...
Oscar Lanzi's user avatar
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2 votes

accurate measurement from inaccurate tools

To add to @Poutnik's and @M.Farooq's answers: Is there a good way to systematically increase the accuracy and precision of a measuring tool using only mathematical means? No, because what you can ...
cbeleites unhappy with SX's user avatar
1 vote

Why isn't residual standard deviation used in FQY analysis?

You do need to account for the absorbance of each sample otherwise the yield will be hugely inaccurate, then take the average etc. Normally you would try to make each solution of the same ...
porphyrin's user avatar
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1 vote
Accepted

Modelling pH as function of time and position

To answer my own question: Using either the diffusion limited or the literature values of the acid-base neutralisation (Baldyga et al., Non-isothermal Micromixing in Turbulent Liquids: Theory and ...
Iridium's user avatar
  • 67
1 vote
Accepted

Current in a Concentration Cell

Yes, your derived expression looks correct to me. As to the closed form for the integral, WolframAlpha is most likely unable to find one because it is simply not there among the elementary and ...
Ivan Neretin's user avatar
  • 31.2k
1 vote

Find molar concentration of sodium carbonate dissolved in water

Use units! Consistently, properly, all the time! You have units all over the place sometimes fitting the quantity you are calculating, most often not. If you approached the problem with correct use ...
Jan's user avatar
  • 68k
1 vote

Does the addition or multiplication rule have precedence deciding the significant figures in 5×5.364?

If the measured width of a rectangle is 5 meters and the length is 5.364 meters, then the area would only have one significant figure, so 30 square meters by the multiplication rule. If you measure ...
DavePhD's user avatar
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