A volume of 50.0 ml of gas is collected by displacement of mercury at 17 degrees Celsius and 760 mm pressure. The mercury level inside the eudiometer is 30.0 mm higher than the outside. What volume will the gas occupy at STP?
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To find the volume the gas will occupy at STP (Standard Temperature and Pressure), we need to use the ideal gas law. The ideal gas law equation 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 the gas
R is the ideal gas constant (0.0821 L·atm/(mol·K))
T is the temperature in Kelvin
First, let's convert the given temperature of 17 degrees Celsius to Kelvin:
T(K) = 17 + 273.15 = 290.15 K
The pressure of the gas given is 760 mm which is equivalent to 760/760 = 1 atm.
Now, we need to find the number of moles of the gas present. To do this, we can use the equation:
n = PV/RT
Substituting the known values:
n = (1 atm × 50.0 mL) / (0.0821 L·atm/(mol·K) × 290.15 K)
n = 0.00178 mol
Now we can calculate the volume the gas will occupy at STP. At STP, the temperature is 273.15 K and the pressure is 1 atm.
Using the ideal gas law equation again:
V(STP) = n(STP) × (R × T(STP))/P(STP)
Substituting the known values:
n(STP) = 0.00178 mol
R = 0.0821 L·atm/(mol·K)
T(STP) = 273.15 K
P(STP) = 1 atm
V(STP) = (0.00178 mol × (0.0821 L·atm/(mol·K) × 273.15 K))/1 atm
V(STP) = 0.0417 L
Therefore, the volume of the gas at STP will be 0.0417 liters (or 41.7 mL).