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Explain why The angle of contact of mercury with glass is obtuse, while that of water with glass is acute

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#### Solution 1

The angle between the tangent to the liquid surface at the point of contact and the surface inside the liquid is called the angle of contact (*θ*), as shown in the given figure.

*S*_{la}, *S*_{sa}, and *S*_{sl} are the respective interfacial tensions between the liquid-air, solid-air, and solid-liquid interfaces. At the line of contact, the surface forces between the three media must be in equilibrium, i.e.,

`cos theta = (S_(sa) - S_(sl))/S_(la)`

The angle of contact *θ* , is obtuse if *S*_{sa} *< S*_{la} (as in the case of mercury on glass). This angle is acute if *S*_{sl}* < S*_{la} (as in the case of water on glass).

#### Solution 2

Let a drop of a liquid L be poured on a solid surface S placed in air A. If T_{SL},and T_{SA} be the surface tensions corresponding to solid-liquid layer, liquid-air layer and solid-air layer respectively and θ be the angle of contact between the liquid and solid ,then

T_{LA} Cos θ + T_{SL} =T_{SA}

=>Cos θ=T_{SA}-T_{SL}/T_{LA}

For the mercury-glass interface, T_{SA}< T_{SL}.

Therefore, cos 0 is negative. Thus θ is an obtuse angle. For the water-glass interface, T_{SA} > T_{SL}. Therefore cos 0 is positive. Thus, θ is an acute angle.