# A syringe containing 1.60mL of oxygen gas is cooled from 95.0∘C to 0.0∘C. What is the final volume of oxygen gas?

In order to determine the change in volume based upon change in temperature we would use

##(V_1)/(T_1) = (V_2)/(T_2)##

From the question we can label what we know and what we are looking for.

##V_1## = 1.60 mL
##V_2## = ?
##T_1## = 95.0 C + 273 = 368.0 K
##T_2## = 0.0 C + 273 = 273 K

Remember for the we must change the celsius temperature to kelvin by adding 273 to each value. This is a great example of why this is necessary. If we use 0.0 C in the denominator we will get no solution.

We can now plug in the values to the equation.

##(1.60 mL)/(368.0 K) = (V_2)/(273.0 K)##

Multiply by 273 on both sides to isolate the variable.

##((273.0 K)(1.60 mL))/(368.0 K) = V_2##

##V_2 = 1.18 mL##

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