A volumetric flask made of Pyrex is calibrated at 20 c. If it is filled to 100ml with 35 c...

Question:

A volumetric flask made of Pyrex is calibrated at 20c. If it is filled to 100ml with 35c acetone, what us the volume of the acetone when it cools to 20c and how significant is the change in the volume of the flask?

Thermal Expansion:

Thermal expansion is the tendency of materials to change shape, length, or volume due to a change in temperature. The thermal expansion can be subdivided into the linear, area, and volumetric thermal expansion. All of the formulas consider that the rate between the change in dimension and the original dimension of the material, and will be equal to the product of the thermal coefficient times the change in the temperature of the object.

$$\dfrac{\Delta V}{V}=\alpha_V\Delta T$$

In order to determine the volume of the acetone, we need to gather the information necessary to solve for the change in volume:

Information:

• Initial volume: {eq}V_0=100\ ml {/eq}
• Initial temperature of acetone: {eq}T_0=35^\circ C {/eq}
• Final temperature of acetone: {eq}T_f=20^\circ C {/eq}
• Thermal expansion coefficient of acetone: {eq}\gamma=0.00143\ C^{-1} {/eq}

We use the volumetric expansion formula to calculate the final volume of the acetone as it cools to 20° C.

{eq}\dfrac{\Delta V}{V}=\gamma\Delta T\\ \Delta V=\gamma V (T_f-T_0)\\ \Delta V=(0.00143\ C^{-1})(100\ ml)(20-35\ C^\circ)\\ \Delta V= -2.145\ ml\\ V_f=V_0+\Delta V\\ V_f=100-2.145\\ V_f=97.855\ ml {/eq}

On the other hand, the volumetric flask will not change its original volume as it is initially at 20° C, and it stays at 20° C. This means that the change in temperature experimented by the flask is almost negligible, and as such, its volume will remain the same.