Understanding the Calculation of Solute Mass from Concentration and Volume

Calculating solute mass from concentration and volume is fundamental in chemistry and engineering. This process converts solution properties into tangible mass values.

This article explores detailed formulas, common values, and real-world applications for precise solute mass determination.

Calculate the mass of NaCl in 2 L of 0.5 M solution.
Find the solute mass in 500 mL of 10% (w/v) glucose solution.
Determine the mass of solute in 1.5 L of 0.2 mol/L H2SO4.
Calculate solute mass from 250 mL of 3% (w/v) saline solution.

Comprehensive Tables of Common Concentration and Volume Values

Concentration Type	Typical Units	Common Values	Volume Range	Example Solutes
Molarity (M)	mol/L	0.01, 0.1, 0.5, 1, 2, 5, 10	0.1 L to 10 L	NaCl, HCl, KOH, H2SO4
Mass/Volume Percent (% w/v)	g/100 mL	0.1%, 1%, 3%, 5%, 10%, 20%	10 mL to 1 L	Glucose, NaCl, Ethanol
Molality (m)	mol/kg solvent	0.1, 0.5, 1, 2, 5	Varies by solvent mass	NaCl, KCl, MgSO4
Normality (N)	eq/L	0.1, 0.5, 1, 2, 5	0.1 L to 5 L	H2SO4, HCl, NaOH
Volume	Liters (L), milliliters (mL)	10 mL, 50 mL, 100 mL, 500 mL, 1 L, 5 L	Varies	Any solution

Fundamental Formulas for Calculating Solute Mass

Calculating the mass of a solute from concentration and volume requires understanding the relationship between these variables. The primary formula is:

mass (g) = concentration × volume × conversion factor

However, the exact formula depends on the concentration units used. Below are the detailed formulas for the most common concentration units.

Molarity-Based Calculation

Molarity (M) is defined as moles of solute per liter of solution. To find the mass of solute:

mass (g) = M × V (L) × MW

M: Molarity in moles per liter (mol/L)
V: Volume of solution in liters (L)
M_W: Molecular weight of solute in grams per mole (g/mol)

Common molecular weights:

Solute	Molecular Weight (g/mol)
NaCl	58.44
H2SO4	98.08
Glucose (C6H12O6)	180.16
KCl	74.55

Mass/Volume Percent (% w/v) Calculation

Mass/volume percent concentration is grams of solute per 100 mL of solution. The formula to calculate solute mass is:

mass (g) = (% w/v) × V (mL) / 100

% w/v: Mass of solute in grams per 100 mL of solution
V: Volume of solution in milliliters (mL)

This formula is straightforward and commonly used in medical and laboratory settings.

Molality-Based Calculation

Molality (m) is moles of solute per kilogram of solvent, not solution. To find solute mass:

mass (g) = m × mass of solvent (kg) × MW

m: Molality in mol/kg
mass of solvent: Mass of solvent in kilograms (kg)
M_W: Molecular weight of solute (g/mol)

Molality is temperature-independent, useful in thermodynamic calculations.

Normality-Based Calculation

Normality (N) is equivalents of solute per liter of solution. The formula is:

mass (g) = N × V (L) × equivalent weight (g/eq)

N: Normality in equivalents per liter (eq/L)
V: Volume in liters (L)
Equivalent weight: Molecular weight divided by n-factor (g/eq)

The n-factor depends on the reaction; for example, H2SO4 has an n-factor of 2 in acid-base reactions.

Detailed Explanation of Variables and Their Typical Values

Concentration (M, % w/v, m, N): Represents the amount of solute per unit volume or mass of solvent. Typical molarity values range from 0.01 to 10 mol/L depending on the solute and application.
Volume (V): The total volume of the solution, usually measured in liters (L) or milliliters (mL). Laboratory volumes often range from milliliters to several liters.
Molecular Weight (M_W): The mass of one mole of solute, expressed in grams per mole (g/mol). This is a fixed property for each compound.
Equivalent Weight: Calculated as molecular weight divided by the n-factor, which depends on the number of reactive units per molecule.
Mass of Solvent: Used in molality calculations, typically measured in kilograms (kg).

Real-World Applications and Case Studies

Case Study 1: Preparing a Sodium Chloride Solution for Medical Use

A hospital pharmacy needs to prepare 500 mL of a 0.9% (w/v) NaCl solution, commonly known as normal saline, used for intravenous infusions. The task is to calculate the mass of NaCl required.

Given:

Concentration = 0.9% (w/v) = 0.9 g per 100 mL
Volume = 500 mL

Using the formula for % w/v:

mass (g) = 0.9 × 500 / 100 = 4.5 g

The pharmacy must weigh 4.5 grams of NaCl and dissolve it in enough water to make 500 mL of solution.

Case Study 2: Calculating Solute Mass in a Sulfuric Acid Solution for Industrial Use

An industrial process requires 2 liters of 1.5 M sulfuric acid (H2SO4). The goal is to determine the mass of H2SO4 needed.