# State two variables that could affect the density of water without changing its form?

Jan 4, 2016

Two of the less obscure variables are temperature and pressure, but I will also talk about the purity of the water.

DENSITY VS. TEMPERATURE

Water and other liquids experience thermal expansion at higher and higher temperatures due to a greater average kinetic energy all-around, disrupting the intermolecular forces. Hence, higher temperatures lead to lower densities.

The following equation allows one to calculate the density of water as it varies with temperature, accurate to five decimal places between ${4}^{\circ} \text{C}$ and ${40}^{\circ} \text{C}$ (Quantitative Chemical Analysis, Harris, pg. 43):

$\setminus m a t h b f \left({\rho}_{\text{H"_2"O}} \approx {a}_{0} + {a}_{1} T + {a}_{2} {T}^{2} + {a}_{3} {T}^{3}\right)$

where ${a}_{0} = 0.99989$, ${a}_{1} = 5.3322 \times {10}^{- 5}$, ${a}_{2} = - 7.5899 \times {10}^{- 6}$, ${a}_{3} = 3.6719 \times {10}^{- 8}$, and $T$ is the temperature in $\text{^@ "C}$.

If you graph this in Excel, you would get, for example, that the density of water at ${22}^{\circ} \text{C}$ is about $\text{0.99778 g/mL}$, while at ${5}^{\circ} \text{C}$ you would see the density as $\text{0.99705 g/mL}$.

The actual densities at ${22}^{\circ} \text{C}$ and ${25}^{\circ} \text{C}$ are $\text{0.9977735 g/mL}$ and $\text{0.9970479 g/mL}$, respectively (Quantitative Chemical Analysis, Harris, pg. 42).

The graph for how the density of water changes according to temperature is like this: DENSITY VS. PRESSURE

Evidently, a larger pressure should make water more dense than it would be at lower pressures because it means a greater degree of compression around the water.

At room temperature (isothermal conditions, ${25}^{\circ} \text{C}$), the molar density $\overline{\rho}$ of water varies according to pressure from $\text{1.00 bar}$ to $\text{40.00 bar}$ in $\text{0.05 bar}$ increments like so: At $\text{1.00 bar}$, the molar density is $\text{55.345 mol/L}$, which is expected. We'll see how to calculate it soon. At $\text{40.00 bar}$, it is $\text{55.442 mol/L}$. So, over a 40-times pressure increase from $1.00$ to $\text{40.00 bar}$, the density of water changed by \mathbf(0.1753%). Not a lot at all!

This is ironically more linear, but there you go. From this straight line, we can generate an equation for the relationship. At ${25}^{\circ} \text{C}$ from $1.00$ to $\text{40.00 bar}$:

$\setminus m a t h b f \left(\overline{\rho} \approx 0.002487 P + 55.345\right)$

Alright, so what the heck is molar density? It's basically the "molarity" of water. (What? Water has a concentration? Yes, it does!)

At ${25}^{\circ} \text{C}$, the density of water is $\text{0.9970479 g/mL}$. So:

$\textcolor{b l u e}{\overline{\rho}} = \left(\text{0.9970479" cancel"g")/cancel"mL" xx ("1000" cancel"mL")/"1 L" xx "1 mol"/("18.015" cancel"g}\right)$

$=$ $\textcolor{b l u e}{\text{55.345 mol/L}}$

PURITY VS. DENSITY

This is kind of a more specific kind of variable, and is not something we necessarily need to worry about for anything other than cleanliness.

Not all water is pure. Sometimes you have calcium and magnesium ions in your water, depending on where you live.

Many research labs have specifically-sourced water called de-ionized water. That way, it is as free of metal-ion contaminants as possible and its density is as accurate as possible.

The more metal-ion contaminants there are, the higher the density would be, because the density is going to be somewhere in between the density of the least dense and of the most dense materials or substances in a mixture or solution, and many metals are more dense than water.

Furthermore, my university's quantitative analysis lab temperature is kept at around ${22}^{\circ} \text{C}$, though others may vary, and the temperature is always monitored by a calibrated thermometer in a styrofoam cup with water in it.