a sample gas has a volume of 200 cubic cm at 25 C and 700 mmHG. If the pressure is reduced to 280 mmHg, what volume would the gas occupy at the same temperature?
What on earth is RPCC? I've never heard of that school subject!
To solve this problem, you can use the combined gas law equation, which relates the initial and final conditions of a gas sample. The combined gas law equation is as follows:
(P1 × V1) / (T1) = (P2 × V2) / (T2)
Where:
P1 and P2 are the initial and final pressures,
V1 and V2 are the initial and final volumes,
T1 and T2 are the initial and final temperatures.
In this case, you are given the initial volume (V1 = 200 cubic cm), the initial temperature (T1 = 25°C), the initial pressure (P1 = 700 mmHg), and the final pressure (P2 = 280 mmHg). You are asked to find the final volume (V2).
Let's plug the given values into the equation and solve for V2:
(P1 × V1) / T1 = (P2 × V2) / T2
Plugging in the known values:
(700 mmHg × 200 cubic cm) / (25°C) = (280 mmHg × V2) / (T2)
Now, we need to convert the temperatures to Kelvin since the equation requires temperatures in Kelvin. The conversion from Celsius to Kelvin is done by adding 273.15.
(700 mmHg × 200 cubic cm) / (25 + 273.15 K) = (280 mmHg × V2) / (T2)
Simplifying further:
(700 mmHg × 200 cubic cm) = (280 mmHg × V2) × (25 + 273.15 K)
Now, divide both sides by 280 mmHg to solve for V2:
(700 mmHg × 200 cubic cm) / (280 mmHg) = V2 × (25 + 273.15 K)
Simplifying further:
(50000 mmHg cm) / (280 mmHg) = V2 × (25 + 273.15 K)
Divide both sides by (25 + 273.15 K):
(50000 mmHg cm) / (280 mmHg × (25 + 273.15 K)) = V2
Now, substitute the values for the initial and final temperatures:
(50000 mmHg cm) / (280 mmHg × (25 + 273.15)) = V2
Calculating further:
(50000 mmHg cm) / (280 mmHg × 298.15 K) = V2
Simplifying:
(50000 cm) / (280 × 298.15) = V2
Now, calculate the right-hand side of the equation:
(50000 cm) / (83642) ≈ 0.597 cm
Thus, the volume of the gas at the same temperature and reduced pressure of 280 mmHg would be approximately 0.597 cubic cm.