Before small batteries were available, carbide lamps were used for bicycle lights. Acetylene gas, C2H2, and solid calcium hydroxide were formed by the reaction of calcium carbide, CaC2, with water. The ignition of the acetylene gas provided the light. Currently, the same lamps are used by some cavers, and calcium carbide is used to produce acetylene for carbide cannons. What volume (in L) of C2H2 at 1.008 atm and 13.2°C is formed by the reaction of 15.72 g of CaC2 with water?
To determine the volume of C2H2 gas formed by the reaction of CaC2 with water, we first need to calculate the moles of CaC2, and then use the balanced equation to relate it to the moles of C2H2 gas. Finally, we can use the ideal gas law to calculate the volume.
Step 1: Calculate the moles of CaC2
The molar mass of CaC2 is:
CaC2: 40.08 g/mol (Ca) + 24.02 g/mol (C2) = 64.10 g/mol
Since we have 15.72 g of CaC2, we can calculate the moles using the formula:
moles of CaC2 = mass / molar mass = 15.72 g / 64.10 g/mol
Step 2: Use balanced equation to relate moles of CaC2 to C2H2 gas
The balanced equation for the reaction of CaC2 with water is:
CaC2 + 2H2O → Ca(OH)2 + C2H2
From the equation, we can see that 1 mole of CaC2 produces 1 mole of C2H2. Therefore, the moles of C2H2 formed will be the same as the moles of CaC2.
moles of C2H2 = moles of CaC2
Step 3: Use the ideal gas law to calculate the volume
The ideal gas law is given by:
PV = nRT
where:
P = pressure (in atm)
V = volume (in L)
n = moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
To use the ideal gas law, we need to convert the temperature from Celsius to Kelvin:
T (Kelvin) = T (Celsius) + 273.15
T (Kelvin) = 13.2°C + 273.15 = 286.35 K
Now, we can rearrange the ideal gas law equation to solve for the volume (V):
V = (nRT) / P
Substituting the known values, we have:
V = (moles of C2H2) * (R) * (T (Kelvin)) / P
Substituting the moles of C2H2 (which are equal to the moles of CaC2), the ideal gas constant (R), the temperature (T), and the pressure (P) given:
V = (moles of CaC2) * (0.0821 L·atm/(mol·K)) * (286.35 K) / 1.008 atm
Now we can substitute the moles of CaC2 calculated in Step 1:
V = (15.72 g / 64.10 g/mol) * (0.0821 L·atm/(mol·K)) * (286.35 K) / 1.008 atm
Calculating this expression will give us the volume of C2H2 gas formed.
To determine the volume of C2H2 gas formed by the reaction, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in L)
n = number of moles of gas
R = ideal gas constant (0.0821 L atm / mol K)
T = temperature in Kelvin
First, let's calculate the number of moles of CaC2 (calcium carbide) that reacted. We can use the molar mass of CaC2 to convert from grams to moles.
Molar mass of CaC2 = (40.08 g/mol) + 2(12.01 g/mol) = 64.08 g/mol
Number of moles of CaC2 = mass of CaC2 / molar mass of CaC2
= 15.72 g / 64.08 g/mol
Next, we need to calculate the number of moles of C2H2 gas that are formed by the reaction. The balanced chemical equation for the reaction is:
CaC2 + 2 H2O → C2H2 + Ca(OH)2
From the equation, we can see that 1 mole of CaC2 reacts to produce 1 mole of C2H2. Therefore, the number of moles of C2H2 is equal to the number of moles of CaC2.
Now we can plug in the values into the ideal gas law equation to calculate the volume:
PV = nRT
V = (nRT) / P
Remember to convert the temperature from Celsius to Kelvin:
T(K) = T(C) + 273.15
P = 1.008 atm
T = 13.2°C + 273.15 = 286.35 K
n = number of moles of C2H2
Plug in the values and solve for V:
V = (nRT) / P
This calculation will give you the volume of C2H2 gas formed by the reaction of 15.72 g of CaC2 with water.