When 0.4300g of NaNO2 is allowed to react with an excess of HSO3NH2, the volume of water is 24.6 degrees celsius and that of the gas is 24.21degress celsius. The atmospheric pressure is 100.72kPa. Calculate the molar volume of N2 at 298.15 K and 100 kPa. You may not use PV=NRT

The volume of the water is 24.6 degrees C? Since when is volume measured in degrees C? Start by writing an equation.

To calculate the molar volume of N2 at the given temperature and pressure, we need to use the Ideal Gas Law equation, which states that:

PV = nRT

Where:
P is the pressure (in kPa)
V is the volume (in m^3)
n is the number of moles
R is the ideal gas constant (8.314 J/(mol·K))
T is the temperature (in Kelvin)

First, let's convert the temperature from degree Celsius to Kelvin:
T1 = 24.6 + 273.15 = 297.75 K
T2 = 24.21 + 273.15 = 297.36 K

Next, we need to calculate the number of moles of N2 produced in the reaction. We know that NaNO2 reacts with HSO3NH2 to produce N2 gas without any other byproducts. Therefore, the moles of N2 produced will be equal to the moles of NaNO2 used.

To find the number of moles of NaNO2, we can use its molar mass (which we need to calculate):
Na (atomic mass) = 22.99 g/mol
N (atomic mass) = 14.01 g/mol
O (atomic mass) = 16.00 g/mol

Total molar mass of NaNO2 = 22.99 + 14.01 + (2 × 16.00) = 69.00 g/mol

Now, we can calculate the number of moles of NaNO2:
moles of NaNO2 = mass / molar mass
= 0.4300 g / 69.00 g/mol

Since we have an excess of HSO3NH2, all the NaNO2 will react to form N2 gas. Therefore, the moles of N2 produced will be the same as the moles of NaNO2 used.

Now that we know the number of moles (n), we can rearrange the Ideal Gas Law equation to solve for the volume (V):
V = (nRT) / P

Plug in the values:
V = (n × R × T2) / P

Remember to convert the pressure to Pascal:
P = 100.72 kPa × 1000 = 100720 Pa

Now we have all the values needed (n, R, T2, and P) to calculate the molar volume of N2:
V = (moles of N2 × 8.314 J/(mol·K) × 297.36 K) / 100720 Pa

Now, you can solve this equation to find the molar volume of N2 at 298.15 K and 100 kPa.