Final answer:
To find the volume of argon at STP, we use the combined gas law and convert initial conditions into standard units before calculating. The final volume of argon at STP is approximately 170 mL.
Step-by-step explanation:
To calculate the volume of argon at standard temperature and pressure (STP), we can use the combined gas law, which relates the pressure, volume, and temperature of a gas. The formula is P1 x V1 / T1 = P2 x V2 / T2, where P is the pressure, V is the volume, T is the temperature in Kelvin, and the subscripts 1 and 2 refer to the initial and final conditions, respectively. STP is defined as 1 atm pressure and 273 K (0°C). First, convert the initial conditions to standard units: 21°C to 294 K and 738 mmHg to 0.97 atm (using the conversion 1 atm = 760 mmHg). The final pressure (P2) is 1 atm (STP), and the final temperature (T2) is 273 K (STP). Plugging the values into the combined gas law and solving for V2:
P1 x V1 / T1 = P2 x V2 / T2
0.97 atm x 183 mL / 294 K = 1 atm x V2 / 273 K
Therefore, V2 = (0.97 atm x 183 mL x 273 K) / (1 atm x 294 K)
V2 ≈ 170 mL
The volume of argon at STP would be approximately 170 mL.