A mass of a gas has a volume of 60cm3 at a temperature of 20°C and a pressure of 785mm mercury. Calculate the volume of a gas at STP(Standard Temperature & Pressure). Given: P1=785mm Hg.
P1V1/T1=P2V2/T2
V2=P1V1*T2/(p2T1)
= (785)*60*273)/(760*293)=57.8cm^3
To calculate the volume of a gas at STP (Standard Temperature and Pressure), we need to use the combined gas law equation. The combined gas law combines Boyle's law, Charles's law, and Avogadro's law.
The equation for the combined gas law is:
(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, we are given:
P1 = 785 mm Hg (pressure at room temperature)
V1 = 60 cm^3 (volume at room temperature)
T1 = 20 °C (temperature at room temperature)
Now we need to find the values at STP. For standard temperature, T2, the value is 0 °C (or 273 K). For standard pressure, P2, the value is 760 mm Hg.
Let's calculate the volume of the gas at STP:
(P1 × V1) / T1 = (P2 × V2) / T2
(785 mm Hg × 60 cm^3) / (20 °C) = (760 mm Hg × V2) / (0 °C)
Now we can rearrange the equation to solve for V2:
V2 = [(P1 × V1 × T2) / (P2 × T1)]
Substituting the values:
V2 = [(785 mm Hg × 60 cm^3 × 273 K) / (760 mm Hg × 293 K)]
Calculating the values:
V2 = 525.29 cm^3
Therefore, the volume of the gas at STP is approximately 525.29 cm^3.
To calculate the volume of the gas at STP (Standard Temperature and Pressure), we need to use the combined gas law equation. The combined gas law equation is:
(P1 x V1)/T1 = (P2 x V2)/T2
Where:
P1 = initial pressure (785 mm Hg)
V1 = initial volume (60 cm3)
T1 = initial temperature (20 °C + 273.15 = 293.15 K)
P2 = final pressure (1 atm, which is the standard pressure at STP)
V2 = final volume (unknown)
T2 = final temperature (273.15 K)
First, let's convert the initial temperature to Kelvin by adding 273.15:
T1 = 20 °C + 273.15 = 293.15 K
Next, we can plug in the given values into the combined gas law equation:
(785 mm Hg x 60 cm3)/293.15 K = (1 atm x V2)/273.15 K
To simplify the equation, let's convert the units of pressure:
1 atm = 760 mm Hg
(785 mm Hg x 60 cm3)/293.15 K = (760 mm Hg x V2)/273.15 K
Simplifying further, the equation becomes:
(47100 mm Hg • cm3) / 293.15 K = (760 mm Hg x V2)/273.15 K
Now, let's solve for V2:
(47100 mm Hg • cm3) / 293.15 K = (760 mm Hg x V2)/273.15 K
Cross multiplying:
(47100 mm Hg • cm3 x 273.15 K) = (760 mm Hg x V2 x 293.15 K)
Simplifying further:
(47100 mm Hg • cm3 x 273.15 K) / (760 mm Hg x 293.15 K) = V2
Calculating:
V2 = (47100 mm Hg • cm3 x 273.15 K) / (760 mm Hg x 293.15 K)
V2 ≈ 54 cm3
Therefore, the volume of the gas at STP is approximately 54 cm3.