Question

A gas has a volume of 55 ml at 37°C and 410 mmHg. Find the final volume at STP.

a) 1.43 L
b) 1.83 L
c) 2.29 L
d) 2.91 L

Answer 1

Using the combined gas law, the final volume of the gas at STP is calculated to be 2.91 L. The initial condition of the gas is given at 37°C and 410 mmHg with an initial volume of 55 ml, and the standard temperature and pressure (STP) are used for the final condition.

Step-by-step explanation:

To find the final volume of a gas at standard temperature and pressure (STP), which is defined as 0°C (273 K) and 1 atm, we can use the combined gas law. Given that the initial volume (V1) is 55 ml, the initial temperature (T1) is 37°C or 310 K (273+37), and the initial pressure (P1) is 410 mmHg, we want to find the new volume (V2) when the gas is brought to STP conditions (P2 = 1 atm or 760 mmHg, T2 = 273 K).

The combined gas law is given by (P1*V1)/T1 = (P2*V2)/T2. Solving for V2 gives us the equation V2 = (P1*V1*T2) / (T1*P2). Plugging in our values we get V2 = (410 mmHg * 55 ml * 273 K) / (310 K * 760 mmHg). Simplifying this, we find that V2 = 2.91 L.

The molar volume of an ideal gas at STP is approximately 22.4 L, which can serve as a useful conversion factor in stoichiometry but is not needed in this calculation.