The surface tension of benzene at 20°C is 28.85 dyne/cm. In a capillary apparatus the liquid rose to a height of 1.832 cm. The density of benzene is 0.8765 g/mL. How would you calculate the diameter of the capillary tube in mm?

1 Answer
Aug 31, 2016

Answer:

The diameter of the capillary tube is 0.366 mm.

Explanation:

One method for measuring the surface tension of a liquid is to measure the height the liquid rises in a capillary tube.

www.chem1.com

The formula is

#color(blue)(|bar(ul(color(white)(a/a) h = "2γcosθ"/"ρgr" color(white)(a/a)|)))" "#

where

#h# = the height the liquid rises in the capillary
#γ# = the surface tension
#θ# = the angle of contact with the surface
#ρ# = the density of the liquid
#g# = the acceleration due to gravity
#r# = the radius of the capillary

We can rearrange the equation to get

#color(blue)(|bar(ul(color(white)(a/a) r = "2γcosθ"/(hgρ)color(white)(a/a)|)))" "#

For most liquids and clean glass, the contact angle #θ# is nearly zero.

If #θ ≈ 0#, then #cosθ ≈ 1#, and the equation reduces to

#color(blue)(|bar(ul(color(white)(a/a) r = "2γ"/(hgρ)color(white)(a/a)|)))" "#

In your problem,

#γ = "28.85 dyne/cm"#
#h = "1.832 cm"#
#ρ = "0.8765 g/mL " = "0.8765 g/cm"^3#
#g = "981 cm·s"^"-2"#

#r = (2 × 28.85 color(red)(cancel(color(black)("dyne·cm"^"-1"))))/(1.832 color(red)(cancel(color(black)("cm"))) × 981 color(red)(cancel(color(black)("cm·s"^"-2"))) × 0.8765 color(red)(cancel(color(black)("g·cm"^"-3")))) × (1 color(red)(cancel(color(black)("g")))·"cm"·color(red)(cancel(color(black)("s"^"-2"))))/(1 color(red)(cancel(color(black)("dyne")))) = "0.0366 cm" = "0.366 mm"#