Question

missed this? watch kcv: simple gas laws and the ideal gas law, iwe: the combined gas law; read section 11.6. you can click on it a cylinder with a moveable piston contains 212 ml of nitrogen gas at a pressure of 1.37 atm and a temperature of 294 k. part a what must the final volume be for the pressure of the gas to be 1.53 atm at a temperature of 337 k? express your answer in milliliters to three significant figures. volume = ml submit previous answers request answer incorrect; try again; 2 attempts remaining ai study tools looking for some guidance? lets work through a few related practice questions before you go back to the real thing this wont impact your score, so stop at anytime and ask for

Explanation:

Step1: Recall Combined Gas Law

The combined gas law is \(\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\), where \(P_1 = 1.37\) atm, \(V_1 = 212\) mL, \(T_1 = 294\) K, \(P_2 = 1.53\) atm, \(T_2 = 337\) K, and we need to find \(V_2\).

Step2: Rearrange formula for \(V_2\)

Rearranging the combined gas law gives \(V_2=\frac{P_1V_1T_2}{P_2T_1}\).

Step3: Substitute values

Substitute the known values: \(P_1 = 1.37\), \(V_1 = 212\), \(T_2 = 337\), \(P_2 = 1.53\), \(T_1 = 294\) into the formula.
\(V_2=\frac{1.37\times212\times337}{1.53\times294}\)

Step4: Calculate numerator and denominator

First, calculate the numerator: \(1.37\times212 = 290.44\); \(290.44\times337\approx97878.28\)
Then, calculate the denominator: \(1.53\times294 = 450.42\)

Step5: Divide numerator by denominator

\(V_2=\frac{97878.28}{450.42}\approx217.3\) (rounded to three significant figures)

Answer:

\(217\) (Note: The more precise calculation gives approximately 217 mL when rounded to three significant figures. The slight difference may be due to rounding during intermediate steps, but the correct calculation should be as follows: \(\frac{1.37\times212\times337}{1.53\times294}=\frac{1.37\times212\times337}{1.53\times294}\approx\frac{1.37\times212\times337}{450.42}\approx\frac{97878.28}{450.42}\approx217\) mL)