# How do I calculate the total volume when i mix 1000 kg of glucose with 5000 L of water

I want to know how to calculate the resulting volume when I mix 1000 kg of glucose into 5000 L of water.

How does the calculation change if I'm mixing NaCl into the water, instead of glucose? Or how does the calculation change if im mixing several things into water (CaCl, Nacl, ect.)?

Sorry if this is a basic question, I have searched alot for a way to calculate this, but could not find answers that clearly explained how to calculate.

• This is something that is usually far easier to just measure than to calculate. There will be tabulated results for common compounds, but, even so, the fastest way to find out is to do the measurement which could easily take less time than the online search required to find a reliable answer. – matt_black Apr 24 at 10:09

## 2 Answers

You could calculate it only if

• you know the density of the substance being dissolved and of the solvent

• there is no interaction between the 2 compounds, causing the deviation from the Raoult law and the shift of the final density.

If both assumptions are met, the final volume is $$V_{\rm mix}=\frac{m_{\rm 1}}{\rho_{\rm 1}}+\frac{m_{\rm 1}}{\rho_{\rm 1}}$$

where m and $$\rho$$ are respective masses and densities.

On the other hand, if the mentioned deviation is in place, the calculation will be wrong.

E.g. if you mix $$\pu{1 L}$$ of ethanol with $$\pu{1 L}$$ of water, then after cooling down ( as the mixture would heat itself), the result will not be $$\pu{2 L}$$, but $$\pu{1.9 L}$$

In such cases, it can be determined experimentally, or from tabulated data of solution densities.

Or, the calculation above can be usually used as a good estimation, especially if there are no significant temperature changes during dissolution.

Density of liquid solutions usually cannot be calculated in a simple way. You need density tables (or a Thermodynamic Activity Coefficient Model like UNIFAC or similar), e.g.:

Bettin, H.; Emmerich, A.; Spieweck, F.; Toth, H.: Density data for aqueous solutions of glucose, fructose and invert sugar. Zuckerindustrie 123 (1998) (5) 341-348

Comesaña, J. F.; Otero, J. J.; García, E.; Correa, A.: Densities and Viscosities of Ternary Systems of Water + Glucose + Sodium Chloride at Several Temperatures. J. Chem. Eng. Data 48 (2003) (2) 362–366

https://www.internetchemie.info/chemie-lexikon/daten/n/natriumchloridloesung-dichtetabelle.php