Good afternoon, Nicolas.
Because this problem involves volume and temperature, we are going to use Charles' Law to solve it.
Charles' Law states that volume is proportional to temperature when pressure is constant. Since pressure is not mentioned in the problem, we are going to assume that it is, in fact, constant.
To use Charles' Law, we have to rely on this formula:
V1 / T1 =V2 / T2
where V1 = initial volume (in liters), V2 = final volume (in liters), T1 = initial temperature (in Kelvin), and T2 = final temperature (in Kelvin).
Step one is going to be the conversion of units.
V1 = 35 ml = 0.035 L
V2 = 55 ml = 0.055 L
T1 = -90°C
K = °C + 273.15
Therefore T1 = -90 + 273.15 = 183.15 K
T2 = unknown
Second, we're going to plug in our known values to the formula:
0.035 L / 183.15 K = 0.055 L / T2
Third, we'll solve. To do this, we can cross-multiply and then determine the unknown variable with some simple algebra:
(0.035) (T2) = (0.055) (183.15)
0.035T2 = 10.07325 (divide both sides by 0.035)
T2 = 287.8 K
Note that we should have four significant figures in our answer because the least precise number in the problem has that many.
Fourth, we have to remember that the problem asks us to provide the final temperature (T2) in degrees Celsius.
°C = K - 273.15
287.8 K - 273.15 = 14.65 °C
T2 = 14.65 °C
Note that this answer does make conceptual sense. As the volume of a gas increased, considering that pressure is constant, it's logical to conclude that the temperature would also be increased. Molecules that are moving with greater energy will take up more space.
