William P. answered • 08/01/19

University Math Instructor and Experienced Calculus Tutor

Hello Justice,

I assume we are dealing with an ideal gas. One common form of the **Ideal Gas Law** is

(Eq.1) **PV = nRT**

where the value of R (the ideal gas constant) depends on the units being used. Before proceeding, it is important to recall that **T must be in Kelvin**. The statement of your problem implies that **n (the amount of gas measured in moles) is constant**. Note that the Ideal Gas Law can be rewritten as

PV/T = nR

If **n is constant, we have**

** PV/T = C**

where C is a constant (whose value in any given problem will depend on n.) This expresses that fact that, **if n is constant, then P is directly proportional to T and inversely proportional to V**. This fact can also be expressed as

(Eq.2) P_{1}V_{1}/T_{1} = P_{2}V_{2}/T_{2}

where P_{1},V_{1}, and T_{1} are the initial pressure, volume, and temperature, respectively, and P_{2},V_{2}, and T_{2} are the corresponding final values. Before completing the problem, let us convert the temperatures to Kelvin. The relationship between temperatures (in Kelvin) and temperatures in degrees Celsius is

T_{K} = T_{C} + 273.15

If T_{1} = 49°C and T_{2} = 17°C, then, on the Kelvin scale, we have

T_{1} = 49 + 273.15 = 322.15K, and

T_{2} = 17 + 273.15 =290.15K

Finally, we can use Eq. 2 to find the final volume V_{2}.

(.942atm)(11.8mL)/322.15K = (.993atm)V_{2}/(290.15K)

which gives

**V**_{2}** ≅ 10.1mL**

Hope that helps! Let me know if you have any further questions.

William