At what temperature will a sample of nitrogen gas with a volume of 328 mL at 15^$\circ$C and 748 mmHg occupy a volume of 0.898 L at a pressure of 642 mm Hg Assume the amount of the nitrogen gas does not change. A) 676^$\circ$C B) 404^$\circ$C C) 396^$\circ$C D) 274^$\circ$C E) 123^$\circ$C

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To solve this problem, we use the combined gas law, which is $P_1V_1/T_1 = P_2V_2/T_2$, where $P$ is pressure, $V$ is volume, and $T$ is temperature in Kelvin. First, we need to convert all units to the correct SI units: volume in liters, pressure in atm (if needed, but here we can keep mmHg since both pressures are given in mmHg), and temperature in Kelvin. The initial temperature is given in Celsius, so we convert it to Kelvin by adding 273.15. The initial conditions are $V_1 = 0.328$ L, $T_1 = 10 + 273.15 = 283.15$ K, $P_1 = 748$ mmHg, and the final conditions are $V_2 = 0.898$ L, $P_2 = 642$ mmHg. We solve for $T_2$, the final temperature in Kelvin, and then convert it back to Celsius if needed. The calculation will show that the final temperature in Kelvin corresponds to the option that, when converted to Celsius, matches one of the choices given.

At What Temperature Will a Sample of Nitrogen Gas with a Volume