Calculate the density of carbon monoxide gas at standard conditions if 25.0 mL of the gas weighs 0.0329 g at 800.00 mm of pressure???
To calculate the density of carbon monoxide gas at standard conditions, we need to follow a series of steps:
Step 1: Convert the given volume from milliliters (mL) to liters (L).
- Since 1 L is equal to 1000 mL, we can divide 25.0 mL by 1000 to get the volume in liters: 25.0 mL ÷ 1000 = 0.025 L.
Step 2: Convert the given weight from grams (g) to kilograms (kg).
- Since 1 kg is equal to 1000 g, we can divide 0.0329 g by 1000 to get the weight in kilograms: 0.0329 g ÷ 1000 = 0.0000329 kg.
Step 3: Calculate the molar mass of carbon monoxide (CO).
- The molar mass of carbon (C) is approximately 12.01 g/mol, and the molar mass of oxygen (O) is approximately 16.00 g/mol.
- Therefore, the molar mass of CO is 12.01 g/mol + 16.00 g/mol = 28.01 g/mol.
Step 4: Use the ideal gas law to calculate the number of moles of carbon monoxide gas.
- The ideal gas law equation is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin (K).
- At standard conditions, the pressure is 1.00 atm and the temperature is 273.15 K.
- Rearranging the ideal gas law equation gives us n = PV / RT.
- Plugging in the values gives us n = (800.00 mm / 760.00 mm/atm) * (0.025 L) / [(0.0821 L·atm/mol·K) * (273.15 K)].
- Simplifying this calculation gives us n = 0.00103 mol.
Step 5: Calculate the density of carbon monoxide gas.
- Density is defined as mass divided by volume (d = m/V).
- Therefore, the density is equal to the weight divided by the volume: density = 0.0000329 kg / 0.025 L.
- Simplifying this calculation gives us a density of 0.00132 kg/L.
So, the density of carbon monoxide gas at standard conditions is approximately 0.00132 kg/L.
To calculate the density of a gas at standard conditions, we need to use the ideal gas law 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)
In this case, we will assume that standard conditions mean a temperature of 273.15 K (0 °C) and a pressure of 1 atm.
Step 1: Convert the given pressure to atm.
The given pressure is 800.00 mm Hg. We can convert it to atm by dividing it by 760 mm Hg/atm:
800.00 mm Hg / 760 mm Hg/atm = 1.0526 atm (rounded to 4 decimal places).
Step 2: Convert the volume to liters.
The given volume is 25.0 mL. We can convert it to liters by dividing it by 1000 mL/L:
25.0 mL / 1000 mL/L = 0.025 L.
Step 3: Calculate the number of moles using the ideal gas law.
Rearrange the ideal gas law equation to solve for n:
n = PV / RT
Substituting the values:
n = (1.0526 atm)(0.025 L) / (0.0821 L·atm/(mol·K))(273.15 K)
n = 0.0298 moles (rounded to 4 decimal places).
Step 4: Calculate the density.
Density is defined as mass divided by volume. We are given the mass (0.0329 g) and the volume (25.0 mL). However, we need to convert the mass to grams before calculating the density.
Convert the mass to grams:
0.0329 g.
Calculate the density:
Density = mass / volume
Density = 0.0329 g / 0.025 L
Density = 1.316 g/L.
Therefore, the density of carbon monoxide gas at standard conditions is 1.316 g/L.