Percentage solution

In biology, the concentration of a solution is often expressed as a "weight/volume percentage" or percentage solution. The percentage is calculated from the weight of solute in grams (g), divided by the total volume of solution in milliliters (mL):

$(Mass(g)/Volume(mL))x100=\%$

A 1% solution would therefore have 1 g of solute dissolved in a final volume of 100 mL of solution. This would be labeled as a weight/volume (w/v) percentage solution. Other types of percentage solutions are weight/weight (w/w) and volume/volume (v/v).

Practical calculations

Conversion to other units

The molarity of a percentage solution (w/v) can be calculated using the molar mass of the solute used. For example, sucrose (table sugar) has a molar mass of a 342.34 g/mol. A 1% sucrose solution (w/v), therefore, is 1 g / 0.1 L / 342.34 g/mol = 0.029 mol/L, or 29 mM. The concentration in gram per litre is easy to calculate: a 1% solution contains 1 g/100 mL or 10 g per/L (1000 mL); therefore, the percentage is to be multiplied by 100.

Making a solution from constituent ingredients

It is common practice in laboratories to make a solution directly from its constituent ingredients. This requires determining the right amount of solvent/solute for specific concentration. There are three cases in practical calculation:

• Case 1: amount of solvent volume is given.
• Case 2: amount of solute mass is given.
• Case 3: amount of final solution volume is given.

In the following equations, A is solvent, B is solute, and C is concentration. Solute volume contribution is considered through ideal solution model.

• Case 1: amount (ml) of solvent volume V_A is given. Solute mass m_B = C V_A d_A /(100-C/d_B)
• Case 2: amount of solute mass m_B is given. Solvent volume V_A = m_B (100/C-1/ d_B )
• Case 3: amount (ml) of final solution volume Vt is given. Solute mass m_B = C Vt /100; Solvent volume V_A=(100/C-1/ d_B) m_B
• Case 2: solute mass is known, V_A = m_B 100/C
• Case 3: total solution volume is know, same equation as case 1. V_A=Vt; m_B = C V_A /100

Example: Make 2 g/100ml of NaCl solution with 1 L water Water (properties). Now, the density information is not required.
m_B = C V_A /100 = 2 x 1000 /100 =20 g

References

• Barry Hinwood, A Textbook of Science for the Health Professions, 2nd Edition. Nelson Thurnes,1992. ISBN 978-0748733774
• Pierre Perrot, A to Z of Thermodynamics. Oxford University Press, 1998. ISBN 978-0198565529