A chemical reaction produced a 0.311 g sample of gas which occupied 225 mL at 55 C exerting a pressure of 886 mm Hg. What is the molar mass of the gas?
you will have to use this two formulas
p*V=n*R*T
n=m/M
p*V=(m/M)*R*T
p*V*M=m*R*T
M=(m*R*T)/P*V
then just make sure you convert units right
(i hope i did convert them right, if not then correct me)
M=(0.311g*8.314L kPa*328.15K)/(mol*K*118.124 kPa*0.225L)
M=31.924 g/mol
Well, to find the molar mass of the gas, we need to do a little bit of math. But don't worry, I promise it won't be as painful as a bad knock-knock joke!
First, we need to find the number of moles of gas. To do this, we can use the ideal gas law equation, which is PV = nRT. Rearranging it, we have n = PV / RT, where P is the pressure, V is the volume, R is the ideal gas constant, and T is the temperature in Kelvin.
Now, let's plug in the values:
P = 886 mm Hg (which we'll convert to atm by dividing by 760),
V = 225 mL (which we'll convert to liters by dividing by 1000),
R = 0.0821 L atm / mol K (the ideal gas constant),
T = 55 + 273 = 328 K (since we need to convert Celsius to Kelvin).
So, n = (886/760) * (225/1000) / (0.0821 * 328).
Next, we calculate the moles using the values and use the formula molar mass = mass / moles. We have the mass (0.311 g), and now we know the number of moles. By dividing the mass by the moles, we can get the molar mass.
Now, my calculations may not be laugh-out-loud funny, but they will help you find the molar mass of the gas. So go ahead and crunch those numbers, and you'll have your answer!
To calculate the molar mass of a gas, we first need to use the ideal gas equation:
PV = nRT
Where:
P = pressure in atm
V = volume in liters
n = number of moles
R = ideal gas constant (0.0821 L•atm/mol•K)
T = temperature in Kelvin
We need to convert the given values into the proper units:
P = 886 mmHg = 886 / 760 atm (since 1 atm = 760 mmHg)
V = 225 mL = 225 / 1000 L (since 1 L = 1000 mL)
T = 55°C = 55 + 273.15 K (since temperature must be in Kelvin)
Now we can rearrange the ideal gas equation to solve for n:
n = PV / RT
Substituting in the values we have:
n = (886 / 760) * (225 / 1000) / (0.0821 * (55 + 273.15))
Calculating this expression will give us the number of moles of the gas.
Next, we can calculate the molar mass using the formula:
Molar mass = mass / moles
Substituting in the given mass of the gas (0.311 g) and the calculated moles, we can calculate the molar mass.
To find the molar mass of the gas, we can use the ideal gas law equation, which relates pressure, volume, temperature, and molar mass.
The ideal gas law equation is:
PV = nRT
Where:
P = pressure in atmospheres (we will need to convert from mm Hg to atm)
V = volume in liters (we will need to convert from mL to L)
n = number of moles of gas
R = ideal gas constant (0.0821 L*atm/(mol*K))
T = temperature in Kelvin (we will need to convert from Celsius to Kelvin)
First, let's convert the pressure from mm Hg to atm:
1 atm = 760 mm Hg
So, the pressure in atm is:
886 mm Hg / 760 mm Hg/atm = 1.1658 atm
Next, let's convert the volume from mL to L:
1 L = 1000 mL
So, the volume in L is:
225 mL / 1000 mL/L = 0.225 L
Now, let's convert the temperature from Celsius to Kelvin:
T(K) = T(C) + 273.15
T(K) = 55°C + 273.15 = 328.15 K
Substituting the given values into the ideal gas law equation:
(1.1658 atm) * (0.225 L) = n * (0.0821 L*atm/(mol*K)) * (328.15 K)
Solving for n (number of moles):
n = (1.1658 atm * 0.225 L) / (0.0821 L*atm/(mol*K) * 328.15 K)
n = 0.0504 moles
To find the molar mass, we can use the formula:
Molar mass (g/mol) = mass (g) / moles
Molar mass = 0.311 g / 0.0504 moles
Molar mass = 6.1643 g/mol
Therefore, the molar mass of the gas is approximately 6.1643 g/mol.