A given mass of gas has a volume of 7.5dm at 250k and 80kmm3,calculate the pressure at which it will have a volume of 7.2dm3 at 270k?
To calculate the pressure at which the gas will have a volume of 7.2 dm³ at 270 K, we can use the ideal gas law equation: PV = nRT.
First, let's convert the initial volume from dm³ to m³:
7.5 dm³ = 7.5 × 10^(-3) m³
Next, let's convert the initial volume from m³ to cm³ (cubic centimeters):
7.5 × 10^(-3) m³ = 7.5 × 10^(-3) × 10^6 cm³ = 7.5 × 10^3 cm³
The temperature is given in Kelvin (K), so no conversion is needed.
Now, let's convert the final volume from dm³ to cm³:
7.2 dm³ = 7.2 × 10^(-3) m³ = 7.2 × 10^(-3) × 10^6 cm³ = 7.2 × 10^3 cm³
We can rearrange the ideal gas law equation to solve for pressure (P):
P = (nRT) / V
Since the mass of the gas is not given, we can assume it to be a constant. Therefore, we can write:
P1 × V1 / T1 = P2 × V2 / T2
Plugging in the values we know:
P1 × 7.5 × 10^3 cm³ / 250 K = P2 × 7.2 × 10^3 cm³ / 270 K
Simplifying the equation:
P1 × 7.5 × 10^3 cm³ × 270 K = P2 × 7.2 × 10^3 cm³ × 250 K
To solve for P2 (the pressure at the final volume and temperature):
P2 = P1 × 7.5 × 10^3 cm³ × 270 K / (7.2 × 10^3 cm³ × 250 K)
Now you can substitute the known values:
P2 = P1 × (7.5 × 10^3 cm³ × 270 K) / (7.2 × 10^3 cm³ × 250 K)
Remember to convert the units to a consistent system (e.g., cm³ and K) before calculating.
If you provide the value of P1 (the initial pressure), I can help you calculate P2 using the given formula.