Final Pressure Calculation for Two Syringes Injected into a Container

Calculation of Final Pressure:

A syringe contains 589 ml of CO at 325 K and 1.2 atm pressure. A second syringe contains 473 ml of N2 at 298 K and 2.6 atm. The goal is to determine the final pressure when the contents of these two syringes are injected into a 1.00 L container at STP.

Final answer: To find the final pressure, divide the total volume by the total moles of gas, and use the ideal gas law to calculate the final pressure.

Explanation:

To find the final pressure when the contents of two syringes are injected into a 1.00 L container at STP, we can use the Ideal Gas Law which states that PV = nRT. We have two different gases - CO and N2 - but we can combine them since they are both at STP. We need to find the total moles of gas in the syringes by dividing the given volumes by the molar volume of gas at STP (22.4 L/mol). Then we can use the combined volume and total moles to find the final pressure using the V1/n1 = V2/n2 ratio.

For the first syringe containing CO:

Volume = 589 mL = 0.589 L

Moles of CO = 0.589 L / 22.4 L/mol = 0.0263 mol

For the second syringe containing N2:

Volume = 473 mL = 0.473 L

Moles of N2 = 0.473 L / 22.4 L/mol = 0.0211 mol

Now we can use these values to find the final pressure:

V1/n1 = V2/n2

(0.589 L + 0.473 L) / (0.0263 mol + 0.0211 mol) = Vfinal / nfinal

0.662 L / 0.0474 mol = Vfinal / nfinal

Vfinal / nfinal = 13.960 L/mol

To find the final pressure, we can use the ideal gas law:

Pfinal = nfinal * R * Tfinal / Vfinal

At STP, Tfinal = 273 K and Vfinal = 1.00 L, so R = 0.0821 L*atm/(mol*K).

Plugging in the values:

Pfinal = (0.0474 mol) * (0.0821 L*atm/(mol*K)) * (273 K) / (1.00 L) = 1.372 atm

Therefore, the final pressure is approximately 1.372 atm.