Answer:
26.3 mL
Step-by-step explanation:
Step 1:
Obtaining an appropriate gas law from the ideal gas equation.
This is illustrated below:
From the ideal gas equation:
PV = nRT
Divide both side by T
PV/T = nR
At this stage, we'll assume the number of mole (n) to be constant.
Note: R is the gas constant.
PV/T = constant.
We can thus, write the above equation as:
P1V1/T1 = P2V2/T2
The above equation is called the general gas equation.
Step 2:
Data obtained from the question. This includes the following:
Initial volume (V1) = 27.5 mL
Initial temperature (T1) = 22.0°C = 22.0°C + 273 = 295K
Initial pressure (P1) = 0.974 atm.
Final temperature (T2) = 15.0°C = 15.0°C + 273 = 288K
Final pressure (P2) = 0.993 atm
Final volume (V2) =..?
Step 3:
Determination of the final volume of the gas using the general gas equation obtained. This is illustrated below:
P1V1 /T1 = P2V2/T2
0.974 x 27.5/295 = 0.993 x V2/288
Cross multiply to express in linear.
295x0.993xV2 = 0.974x27.5x288
Divide both side by 295 x 0.993
V2 = (0.974x27.5x288)/(295x0.993)
V2 = 26.3 mL
Therefore, the new volume of the gas is 26.3 mL