The enthalpy of vaporization of benzene, C6H6(l), is 33.9 kJ mol?1 at 298 K. How many liters of C6H6(g), measured at 298 K and 88.7 mmHg, are formed when 1.90 kJ of heat is absorbed by C6H6(l) at a constant temperature of 298 K?

not sure what formulae to use, thanks!

M = Q/([heat of vaporization)
1.90 kJ/ 33.9 kJ/mol = 0.056 moles

Use the perfect gas law to covert that number of moles to liters of gas. Be sure to use the low pressure of 88.7 mm Hg

sweet dude got it

ihope thx

PV = nRT

0.056 moles * 0.0821 L atm K-1 mol-1 * 298 K = 11.3 L

To convert the number of moles of benzene, C6H6, to liters of gas at a specific temperature and pressure, you can use the ideal gas law. The formula for the ideal gas law is:

PV = nRT

Where:
P is the pressure in atmospheres (convert mmHg to atm if necessary)
V is the volume in liters
n is the number of moles
R is the ideal gas constant (0.0821 L·atm/(K·mol))
T is the temperature in Kelvin

First, let's convert the pressure from mmHg to atm. Divide the given pressure (88.7 mmHg) by 760 mmHg/atm.

88.7 mmHg / 760 mmHg/atm = 0.1167 atm

Next, we have the number of moles of C6H6 which is 0.056 moles.

Now, we can rearrange the ideal gas law equation to solve for V:

V = (nRT) / P

Substituting the known values:

V = (0.056 mol * 0.0821 L·atm/(K·mol) * 298 K) / 0.1167 atm

V = 0.348 L

So, approximately 0.348 liters of C6H6 gas would be formed when 1.90 kJ of heat is absorbed by C6H6(l) at a constant temperature of 298 K and 88.7 mmHg pressure.

To convert moles of benzene to liters of gas, you can use the ideal gas law. 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.

In this case, you have the number of moles of benzene (0.056 mol), the pressure (88.7 mmHg), and the temperature (298 K). You need to solve for the volume (V).

Convert the pressure from mmHg to atm:
88.7 mmHg × (1 atm / 760 mmHg) = 0.1168 atm

Plug in the values into the ideal gas law equation:
(0.1168 atm) × V = (0.056 mol) × (0.0821 L·atm/mol·K) × (298 K)

Simplify and solve for V:
V = (0.056 mol) × (0.0821 L·atm/mol·K) × (298 K) / 0.1168 atm

V ≈ 11.8 liters

Therefore, approximately 11.8 liters of C6H6(g) would be formed when 1.90 kJ of heat is absorbed by C6H6(l) at a constant temperature of 298 K.