How do I convert salinity measured in mg/L Cl into parts per thousand as NaCl?

I have collected water data using a refractometer that records salinity in ‰ (parts per thousand) as $\ce{NaCl}$. I want to compare my data to other data but every journal article I read has the results in $\pu{mg/L }\ce{Cl-}$


How do I convert my $\pu{ppt}$ data into $\pu{mg/L}$ or vice versa so I am comparing apples to apples?




$$\pu{1 mg L-1} = \pu{1 ppm} = \frac{1}{1000}\cdot\pu{ppt}$$


or


$$\pu{1 ppt} = \pu{1000 ppm}$$


For example:


$$\pu{10 ppm} = \frac{10}{1000}~\pu{ppt} = \pu{0.01 ppt}\tag{1}$$
$$\pu{5 ppt} = 5\cdot\pu{1000 ppm} = \pu{5000 ppm}\tag{2}$$


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There is problem with ppx values they are ambiguous. It may be w/w, w/v, v/v, n/n. 


Salt water has density significantly different to $\pu{1 g/ml}$, so $\pu{1 ppt(parts per thausand) }$ may mean $\pu{1000 mg/L}$ or $\pu{1000 mg/kg}$, with the recalculation factor of the solution density.


The former ($\pu{ppt w/v as 1000 mg/L}$) is more probable, but check it. E.g prepare a salt solution of known concentration and check, in which ppt variant is your refractometry measurement calibrated.


$$\pu{1 ppt(w/v)} = \pu{1000 mg/L}$$


$$\pu{1 ppt(w/w) = 1000 mg/kg = \frac{\pu{1000 mg/L}}{ \rho(\pu{g/mL})} }$$


where $\rho$ is density of solution in $\pu{g/ml}$


$\pu{1000 mg NaCl}$ is equivalent to $1000\cdot \frac {M\_{\ce{Cl}}} {M\_{\ce{Na}}+
M\_{\ce{Cl}}}=\frac {35.453}{22.990+35.453}=\pu{606.6 mg Cl }$


$$\pu{1 ppt NaCl(w/v)} = \pu{606.6 mg/L Cl}$$


$$\pu{1 ppt NaCl(w/w) = \frac{\pu{606.6 mg/L Cl}}{ \rho(\pu{g/mL})} }$$


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