Please!!! its extremely urgent. i do not need answers, only how to do it
A sample of nitrogen gas (N2) kept in a container of volume 10.1 L and at a temperature of 20.3°C exerts a pressure of 3.1 atm. Calculate the number of grams of gas present. Round to one decimal place, do not include units in your answer.
2) A volume of 0.194 L of a gas at STP weighs 0.545 g. Calculate the molar mass of the gas. Round to one decimal place do not include units.
1) Use PV = nRT and solve for n = moles N2. Then n = grams/molar mass, solve for grams.
2) Remember 1 mole of a gas at STP occupies 22.4L, use that to convert 0.194 L to moles. Then moles = grams/molar mass. You know moles and molar mass, solve for grams.
To solve these problems, you will need to use the ideal gas law equation, which is:
PV = nRT
Where:
- P is the pressure of the gas
- V is the volume of the gas
- n is the number of moles of gas
- R is the ideal gas constant (0.0821 L·atm/(mol·K))
- T is the temperature in Kelvin
Let's go step by step:
1) To calculate the number of grams of gas present:
a) Convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 20.3 + 273.15 = 293.45 K
b) Rearrange the ideal gas law equation to solve for moles:
n = PV / RT
c) Calculate the number of moles:
n = (3.1 atm) * (10.1 L) / (0.0821 L·atm/(mol·K)) * (293.45 K)
d) Convert moles to grams using the molar mass of nitrogen (28.0134 g/mol):
grams = n * molar mass
grams = (number of moles) * (molar mass)
2) To calculate the molar mass of the gas:
a) Convert the volume from liters to m³:
V(m³) = V(L) / 1000
V(m³) = 0.194 L / 1000 = 0.000194 m³
b) Rearrange the ideal gas law equation to solve for moles:
n = PV / RT
c) Calculate the number of moles:
n = (1 atm) * (0.000194 m³) / (0.0821 L·atm/(mol·K)) * (273.15 K)
d) Calculate the molar mass:
molar mass = (weight of gas) / (number of moles)
Please note that in both cases, the units will cancel out correctly, leaving you with the desired units as a result.