The density of a gas at s.t.p is 1.3kg/m3. Find the density of the gas at -15 degree celcius and at a pressure of 8cmHg.
To find the density of a gas at a different temperature and pressure, we can use the ideal gas law and the concept of the ideal gas state.
The ideal gas law is expressed as:
PV = nRT
where:
P is the pressure of the gas
V is the volume occupied by the gas
n is the number of moles of the gas
R is the ideal gas constant
T is the temperature of the gas in Kelvin
Let's break down the problem step by step:
Step 1: Convert the given values to the correct units.
- The temperature is given in degrees Celsius, so we need to convert it to Kelvin. To do this, we add 273.15 to the temperature value:
T = -15°C + 273.15 = 258.15 K
- The pressure is given in cmHg, so we need to convert it to SI units (Pascal or Pa). We know that:
1 cmHg = 133.3224 Pa (approximately)
Therefore, the pressure in Pa is:
P = 8 cmHg × 133.3224 Pa/cmHg = 1066.6 Pa
Step 2: Calculate the gas constant (R)
- The value of the ideal gas constant is R = 8.314 J/(mol·K). However, for the calculation of density, we need R in the units of m3·Pa/(K·mol). To convert, we divide R by the molar mass of the gas.
Step 3: Calculate the number of moles (n) using the ideal gas law
- Rearranging the ideal gas law equation, we get:
n = PV / (RT)
Step 4: Calculate the new volume (V)
- Since we are dealing with the same amount of gas, the moles (n) will remain constant. So, we can use the relationship between pressure, volume, and temperature (Boyle's Law) as:
P1V1 / T1 = P2V2 / T2
Rearranging and substituting the known values:
P2 = 1066.6 Pa
T2 = 258.15 K (from Step 1)
P1 = 1 atm (standard pressure at STP)
V1 = 1 m3 (standard volume at STP)
Solving for V2:
V2 = (P1V1 × T2) / (T1 × P2)
Step 5: Calculate the density (ρ)
- Density is defined as mass per unit volume. We can calculate it using the equation:
ρ = m / V
Since density is the primary unknown, we can rewrite this equation as:
ρ = (P × MW) / (R × T)
Where:
P is the pressure in pascal (Pa) (from Step 4)
MW is the molecular weight of the gas
R is the ideal gas constant (in the correct units)
T is the temperature in Kelvin (from Step 1)
Step 6: Substitute the known values and calculate the density
- The molecular weight of the gas is not given in the question. Therefore, you need to provide it in order to calculate the density accurately.
By following these steps, you can calculate the density of the gas at -15 degrees Celsius and a pressure of 8 cmHg. Remember to substitute the correct values and units for each variable and perform the calculations accordingly.