The National Institute of Science and Technology (NIST) kinetics database lists the rate constant, k, of a particular gaseous reaction as 8.56× 10–10 cm3·molecule–1·s –1 at 298 K. convert to units of M-1 s-1. convert rate constant to units of Torr-1 s-1. What is the order of this reaction?

To convert the rate constant, k, from cm3·molecule–1·s –1 to M-1 s-1, we need to use the Avogadro's number, Nₐ, which is approximately 6.022 × 10²³.

Step 1: Convert from cm3·molecule–1·s –1 to m3·molecule–1·s –1:
The conversion factor is 1 cm3 = 1 × 10⁻⁶ m3, so
k (m3·molecule–1·s –1) = 8.56 × 10⁻¹⁰ cm3·molecule–1·s –1 × (1 × 10⁻⁶ m3 / 1 cm3)
k (m3·molecule–1·s –1) = 8.56 × 10⁻¹⁶ m3·molecule–1·s –1

Step 2: Convert from m3·molecule–1·s –1 to M-1 s-1:
The conversion factor is 1 m3 = 10⁶ L, and 1 L = 10³ cm3. Therefore,
k (M-1 s-1) = k (m3·molecule–1·s –1) × (10⁶ L / 1 m3) × (10³ cm3 / 1 L)
k (M-1 s-1) = 8.56 × 10⁻¹⁶ m3·molecule–1·s –1 × (10⁶ L / 1 m3) × (10³ cm3 / 1 L)
k (M-1 s-1) = 8.56 × 10⁻¹ M-1 s-1

Step 3: Convert from M-1 s-1 to Torr-1 s-1:
The conversion factor is 1 atm = 760 Torr. Therefore,
k (Torr-1 s-1) = k (M-1 s-1) × (1 atm / 760 Torr)
k (Torr-1 s-1) = 8.56 × 10⁻¹ M-1 s-1 × (1 atm / 760 Torr)
k (Torr-1 s-1) ≈ 1.127 × 10⁻³ Torr-1 s-1

Now, to determine the order of the reaction, we need more information about the overall reaction equation and the reactants involved. The order can be determined by analyzing the rate law expression, which provides information about how the concentration of a reactant affects the rate of the reaction.

To convert the rate constant from cm3·molecule–1·s–1 to M–1·s–1, you need to keep in mind that 1 M is equal to 1 mole per liter (mol/L). Given that 1 cm3 is equal to 10–6 L, and the molecular weight of the molecule is needed to convert from moles to Molarity.

Let's use an example molecular weight of 28 g/mol for the molecule in question.

1. Convert cm3 to L:
1 cm3 = 10^-6 L

2. Convert molecules to moles:
Divide the rate constant by Avogadro's number (6.022×10^23 molecules/mol) to get the rate constant in moles:
k (in moles) = k (in cm^3·molecule^-1·s^-1) / Avogadro's number

3. Convert moles to Molarity:
Convert from moles to liters (L) by multiplying by the inverse of the molarity (M):
Molarity (M) = moles / volume (L)

Since 1 M = 1 mol/L, we need to divide the result by the volume in liters to get the rate constant in M–1·s–1:
k (in M-1·s-1) = k (in moles) / volume (L)

4. Considering the molecular weight:
If the molecular weight (MW) of the molecule is known, you can convert from moles to Molarity:
Molarity (M) = moles / volume (L)
Molarity (M) = (moles / MW) / volume (L)

Thus, the final calculation becomes:
k (in M-1·s-1) = k (in moles) / (volume (L) x MW)

To convert the rate constant from cm^3·molecule^–1·s^–1 to Torr^–1·s^–1, we need to use the ideal gas law to relate the pressure (P) and volume (V) to the concentration (c).

The ideal gas law equation is given by:
P × V = n × R × T

Where:
P = pressure (in Torr)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/K·mol)
T = temperature (in Kelvin)

Rearranging the equation:
n/V = P / (R × T)

To convert the rate constant from cm^3·molecule^–1·s^–1 to Torr^–1·s^–1, we multiply by the conversion factor n/V, where n is the number of moles and V is the volume:

k (in Torr^–1·s^–1) = k (in cm^3·molecule^–1·s^–1) × n/V

Now, let's find the order of the reaction. The order of a reaction can be determined by examining the units of the rate constant.

If the units of the rate constant are in M^-1*s^-1, it indicates a first-order reaction.
If the units of the rate constant are in M^-2*s^-1, it indicates a second-order reaction.
If the units of the rate constant are in M^-3*s^-1, it indicates a third-order reaction.

Since the rate constant units were converted to M^-1*s^-1, we can conclude that the order of the reaction is first-order.

Remember to substitute the actual values of Avogadro's number and the molecular weight in the conversions.

Please note that the example molecular weight provided (28 g/mol) may not be accurate for your specific reaction, so make sure to use the correct molecular weight in your calculations.

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