 Magnetic Susceptibility Balance Frequently Asked Questions             # Why does my MnCl2.4H2O solution filled tube that accompanied my MK1 MSB vary its reading?

Like many paramagnetic species, the reading MnCl2 solution gives is dependent on temperature. Always note the temperature when you measure the MnCl2 containing tube. Refer to the Mk1 manual for how to correct for sample temperature.
If the reading changes over time despite the temperature remaining constant, then it is possible that there is a tiny hole in the seal which is allowing gas to escape thereby altering the concentration and reading.

# Why can't you tell me the concentration of MnCl2.4H2O in the solution in the tube?

The concentration of MnCl2.4H2O is known to be approximately 1M at the time of manufacture but, because it is adjusted to match a reference sample the final concentration in the sealed tube cannot be precisely known due to the method of manufacture.

Each tube is sealed by hand and it is not possible to guarantee that there is no tiny gas leak which over time will cause the concentration to change due to solvent evaporation. If the length of liquid in the tube has reduced since it first arrived - it should be at least 2.0cm - then the readings will be suspect. An air lock can sometimes trap some liquid at the top of the tube so always make sure that all of the liquid is together at the bottom of the tube before checking the length.

# How can I use the MnCl2.4H2O tube to monitor the performance of the MK1 balance?

Regular measurement of the tube and recording of the temperature of measurement will allow confidence to be gained that the tube is gas tight. A plot of temperature versus tube reading should give a straight line. Ideally, keep the tube with the balance so that they are at the same temperature.

# How do I know if the reading I'm getting is right?

To work out if the balance is reading the 'right' number for a sample you have to check that it gives the right reading for a pure substance with a known magnetic susceptibility or a solution of such a substance with a pure solvent of known magnetic susceptibility. For the latter see How do I work out the concentration of the solute in the liquid sample?, below. A good start would be to use the standard tube delivered with your instrument subject to the three answers above. Consider the choice of known substance carefully. Using solid substances in powder form requires allowances for the actual density of sample in the sample tube at time of measurement. Other things to bear in mind are; that the susceptibility of many paramagnetic species is temperature dependent, the ideal substance should measure a little bit higher than the highest expected test sample, liquids are easier to measure reliably.

# What is the relationship between Molar Magnetic Susceptibility and Mass Magnetic Susceptibility?

For a pure compound the Mass Susceptibility is equal to the Molar Susceptibility divided by the molecular mass of the substance.

# What are the different types of susceptibility and how are these related?

There are 3 commonly used types of susceptibility each with its own symbol. These types are shown below together with how they are related to each other in the cgs system are:

 Xv Volume susceptibility Xv = Xg ✴ ρ and Xv = XM ✴ ρ / M Xg Mass susceptibility Xg = Xv / ρ and Xg = XM / M XM Molar susceptibility XM = Xv ✴ M / ρ and XM = Xg ✴ M Where: ρ is the substance density in gmcm-3 e.g. water 0.9982 gmcm-3 (20°C) M is the relative molecular mass e.g. water 18gm/mol

Literature values of susceptibility are often quoted as XM - Molar susceptibility, sometimes described as susceptibility per gram formula weight.

# How do I work out if two tubes are matched?

At the simplest level two tubes are 'matched' if they give the same reading in the instrument when clean and empty. For very precise work you can go further and check that they give the same reading when filled with the same volume of a sample - for example pipette 300µl of 1M MnCl2 solution into each clean tube and put them in the balance. Rotate the tube about a clock face and record the results. Calculate the mean for each tube. If the means agree then the tubes can be said to be matched.
At a more detailed level matching tubes is usually intended to save having to empty and clean a tube to measure another sample under identical conditions. Tubes would be said to be matched if the readings obtained with them were the same for all samples. This requires the tubes to pass (at least) 2 tests
• The readings of the tubes are the same when they are empty
• The readings of the tubes when containing identical samples are the same
If both apply then the tubes are matched.
If the empty tubes read the same but filled tubes do not this indicates that the sample space defined by the insides of the tubes are different although the amount of glass being measured is the same.
If the filled tubes read the same but the empty tubes do not this indicates that the sample space defined by the insides of the tube is consistent between the tubes but the amount of glass being measured is different.
The explanation of how these situations can occur is that the key quality control dimension of this process is the distance from the inside of the closed end to the lower end of the rubber sleeve around the upper part of the tube which doesn't necessarily account for the shape of or amount of glass in the closed ends of the sample tubes (see 2 examples in picture below) which are are formed by hand. # How do I measure strong samples which are over range?

The instrument reading is related to the volume of sample in the measuring space. This means that one answer for samples that are over range is to put less material between the magnets whilst maintaining a depth of at least 1.5cm. For a soluble substance it is simply a matter of dissolving it and diluting until the reading is in range. For large dilution ratios the presence of the solvent can easily be accounted for by measuring the sample using a tube containing just the solvent and set the display to read 000 with the zero knob before measuring the diluted sample. Prepare the same dilution ratio of all the samples and the results will be relative and directly comparable.
For smaller dilution ratios refer to the principles described in How do I work out the concentration of the solute in the liquid sample?

If the sample is not soluble (or if you prefer) then a narrower tube could be used to present less of the sample to the instrument. Sherwood can provide tubes of 1 or 2mm internal diameter which would reduce the readings by 1:10.5 and 1:2.62 respectively, relative to the same substance in a normal tube of 3.24mm i.d.
For insoluble samples an alternative that is sometimes possible is to mix the sample with an inert substance with low mass susceptibility. It is important that the mixing is very thorough and this may not be easily achieved. One inert solid 'diluent' used has been icing sugar. Again it is necessary to account for the presence of the diluent. For large dilution ratios this can be most simply done by setting zero with the tube containing just the diluent. For smaller dilutions refer to the principles described in How do I work out the concentration of the solute in the liquid sample?

# How do I work out the concentration of the solute in the liquid sample?

The simple answer is to plot a 2-point linear calibration from the MSB readings (R-R0) of
1. a solution of known concentration, and
2. the pure solvent with no solute in
The equation of this line will allow us to calculate the concentration of a solution of unknown concentration from its reading.
Here's an example based on aqueous solutions of MnCl2.4H2O. Ideally the same tube should be used for all measurements and, if doing so, it should be rinsed carefully a number of times with the fresh solution and tipped to waste so that the solution in the tube isn't contaminated by the previous solution measured. At the start take a reading for the empty sample tube; this will be R0 that has to be subtracted from the readings of the other samples to give the (R-R0) values below.
For sample 1 we choose a 1M aqueous solution of MnCl2.4H2O made with 197.9gm (molecular mass) made up to 1 litre in water and get a reading that gives (R-R0) of 1149.
Sample 2 is water and its reading gives an (R-R0) of -59.
We plot these 2 points on our graph and draw a straight line connecting them as below. The equation of this line is (R-R0) = (1208 ✴ conc) - 59
Which we can rearrange to calculate concentration from (R-R0), thus Our unknown solution gives a (R-R0), reading of 1000 so its concentraion is

(1000+59) / 1208=0.877 M

This process can be followed on the graph by starting with the red value of 1000 on the (R-R0) axis traced horizontally across to meet the calibration line then, in blue, followed vertically down to the concentration axis at a value of 0.88M.

A more detailed explanation from first principles and using literature values instead of having to make a solution of known concentration is also available on this page under the question How do I work out the expected MSB reading of a solution of a known solid in a known solvent?

# What about the 'air correction term'?

Some chemists use an air correction term to account for the displacement of air in the balance when a sample is introduced. The air correction term makes a very small contribution to results, is referred to in section 1.1 of the Mk1 manual and the equation for it is given in Appendix A to that manual.

# Why do I need to add 1.5cm depth of sample?

The section of the tube which is 'exposed' to the measuring magnetic field inside the instrument extends to just less than 1.5cm up from the bottom of the tube.
More information is also available on this page under the question Is it ever possible to work with less than the 1.5cm depth?

# Is it ever possible to work with less than the 1.5cm depth?

It can be possible to get reliable relative readings with a depth of sample less than 1.5cm in the tube, however samples can only be compared to one-another when the same volume (not mass) is put in the bottom of the tube. Due to this constraint it is probably only suitable to fixed volumes of liquid that can be precisely pipetted into the bottom of the tube. When the depth of sample is > 1.5cm the reading is proportional to the sample Xv (volume susceptibility). Below 1.5cm the reading becomes a function of Xv and the sample volume. Any difference in volume will cause an error in the relative reading that is not necessarily proportional to the sample volume.

# Are the MSBs able to measure high or low temperature samples?

Neither the MK1 or Auto Magnetic Susceptibility Balances have temperature control but it is possible to put hot or cold samples into either instrument and get readings.
Measurements made on such samples will be subject to errors for two reasons; the sample temperature will not be constant so any temperature dependent magnetic property will be changing and there are magnets inside the balance, very close to the sample, whose strength varies as these are heated or cooled by the sample. The user would have to make allowance for these effects. If any form of sensor is in the sample to measure its temperature to help with interpreting the readings then the effect of the sensor itself on the magnetic measurement must be understood.

# How do I work out the expected MSB reading of a known, solid substance?

To do this using first principles and literature values, and without doing any measurements we will need some fundamental relationships involving magnetic susceptibility so let's start with these.

Literature values of susceptibility are often quoted as Molar susceptibility, XM which is related to Mass susceptibility, Xg by the formula Mk1 readings for samples, in a standard sample tube with an internal diameter of 0.324cm, are related to Mass susceptibility by the formula printed on the instrument top panel Where: C is the balance constant that is factory set at 1.0 l, m are the length of sample in the tube, in cm and sample mass, in g. R The balance reading for the sample and tube R0 The balance reading for the empty tube

Now we can go from the susceptibility of a known substance to its reading on the Mk1 balance.

Take for example the compound MnCl2.4H2O of relative molecular mass M = 197.9 and literature Molar susceptibility XM of +14,600 x10-6 cgs at 20°C. We start by converting this to Mass susceptibility using, from above, equation i In our thought experiment we do not have a length or mass for equation ii, but we can fnd the literature value for the density of our substance, 2.01gmcm-3. Knowing that a standard 0.324cm internal diameter sample tube has a crosssectional area 0.0824cm2 and that the volume of a cylinder is equal to the cross sectional area multiplied by its length, we can rearrange the formula for density, ρ To get our final answer we substitute these numerical values into equation ii This would lead us to expect an MSB reading of +1222 on the x10 scale. This reading would be for a solid cylinder that fills the standard sample tube. In practice we are likely to be using a powder sample with a density smaller than the literature value and will therefore get a proportionally smaller MSB reading. To correct for this, without having to measure the actual sample density, equation ii conveniently allows us to measure just l and m. Let's say we get l = 2.2cm and m = 0.193g. Now we can calculate, for the sample that we are measuring, a value for the effective density  Were we doing a practical experiment we would get the same result by substituting these measured values of l and m directly into equation ii as follows Thus # How do I work out the expected MSB reading of a solution of a known solid in a known solvent?

To do this we will need some fundamental relationships involving magnetic susceptibility so let's start with these.

Literature values of susceptibility are often quoted as Molar susceptibility, XM which is related to Mass susceptibility, Xg by the formula The Mass susceptibility, Xs of a solution of a single solute in a single solvent is made up of the relative contributions from the solute and solvent according to the formula Where: m1, m0 are the masses of solute and solvent respectively in the solution Xg, X0 are the Mass susceptibilities of the solute and solvent respectively

Mk1 readings for samples in a standard sample tube with an internal diameter of 0.324cm are related to Mass susceptibility by the formula printed on the instrument top panel Where: C is the balance constant that is factory set at 1.0 l, m are the length of sample in the tube, in cm and sample mass, in g. R The balance reading for the sample and tube R0 The balance reading for the empty tube

Now we can go from the susceptibility of a known concentration to its reading on the Mk1 balance.

Take for example MnCl2.4H2O of relative molecular mass M = 197.9 dissolved in water, M = 18. The literature Molar susceptibilities, XM are respectively +14,600 and -12.96 x10-6 cgs at 20°C which convert to Mass susceptibility using, from above, equation i To use equation ii we also need to know m1 and m0. These will come from the solution concentration. Let's choose a 1M aqueous solution. This would contain 197.9gm of solute made up to 1 litre with water. We would fnd that 10cm3 of the solution would weigh 11.03gm so the 1 litre contained (1103-197.9) = 905.1 gm of water and had a density, ρ of 1.103 gmcm-3

With m1 = 197.9 and m0 = 905.1 we can calculate the Mass susceptibility of our 1M solution of MnCl2.4H2O by substituting these numerical values into equation ii In this thought experiment we do not have a length or mass to use in equation iii. We do however have the density of our solution, 1.103 gmcm-3. Knowing that a standard 0.324cm internal diameter sample tube has a cross-sectional area 0.0824cm2 and that the volume of a cylinder is equal to the cross sectional area times its length, we can rearrange the formula for density, ρ The final step is to substitute these numerical values into equation iii So the answer to our question is that we would expect a 1M aqueous solution of MnCl2.4H2O to give an MSB reading of 