Suppose that you have a vial of an unknown liquid. You are trying to determine i

Question

Suppose that you have a vial of an unknown liquid. You are trying to determine its identity by studying how its volume changes with temperature. You fill a Pyrex graduated cylinder to 100.00 mL with the liquid when the liquid and the cylinder are at 0 C. You then raise the temperature to 50 C, allowing the graduated cylinder and liquid to come to equilibrium at each temperature. The final reading of the graduated cylinder of the water is 102.46 mL.

Using the subscript l for the liquid and g for the glass, determine an equation for the apparent volume of the liquid. Take Vo to be the initial volume of the liquid when the liquid is at 0.000 C.

Use the fact that DV = Vo b DT

bg = 9x10-6 C-1

Based on your previous result, should there be a linear relationship between temperature and volume? If so, what would the slope m of the line be in terms of the initial volume of the liquid and the coefficients of expansion for the glass and liquid? Use this equation for the slope to find an expression for the coefficient of expansion of the liquid, bl.

Explanation / Answer

change in volume of liquid = 102.46-100 =2.46 ml, Vo =initial volume= 100ml,

temperature difference= 50-0 = 50 deg.c

hence change in volume = 2.46= V0*(1+alpha*50)=100*(1+alpha*50)

alpha = coefficient of volume expansion

2.46/100 = alpha*50

alpha= 2.46/(100*50)= 0.000492ml/deg.c, this is the slope.

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