the specific heat of a gas is found to be 0.075 calories at constant volume & its formula weight is 40. the atimicity of the gas is ............

cv=.075/40=3=3/2R

therefore monoatomic

The first time you posted this I asked if you had a definition for atomicity. Google says on the Internet that atomicity is a synonym for valence but I don't get the connection. I may be able to help IF you tell me what atomicity is.

To find the atomicity of a gas, we need to know its specific heat at constant volume. Given that the specific heat (Cv) of the gas is 0.075 calories, we can use the formula:

Cv = (9/2) × R × (atomicity - 1)

where R is the universal gas constant (8.314 J/mol·K).

Let's convert the given specific heat from calories to joules:

1 calorie = 4.184 joules

Therefore, the specific heat in joules is:

0.075 calories × 4.184 joules/calorie = 0.3138 joules

Now we can solve for the atomicity:

0.3138 joules = (9/2) × 8.314 J/mol·K × (atomicity - 1)

Simplifying the equation:

(9/2) × 8.314 × (atomicity - 1) = 0.3138

Dividing both sides by (9/2) × 8.314:

atomicity - 1 = 0.3138 / [(9/2) × 8.314]

atomicity - 1 ≈ 0.003556

Adding 1 to both sides:

atomicity ≈ 1 + 0.003556

atomicity ≈ 1.003556

Since the atomicity of a gas must be a whole number, we can approximate it to the nearest whole number:

atomicity ≈ 1

Therefore, the atomicity of the gas is approximately 1.

To find the atomicity of the gas, we need to gather the relevant information and use the concept of specific heat at constant volume.

Given:
Specific heat of the gas (Cv) = 0.075 calories
Formula weight of the gas (molar mass) = 40

Now, let's understand the concept of atomicity and its relation to specific heat at constant volume. Atomicity refers to the total number of atoms present in one molecule of a substance. For gases, the specific heat at constant volume (Cv) can be given as:

Cv = (0.5 * R) * (atomicity)

Where:
R is the molar gas constant

However, since we are given the specific heat in calories, we need to convert it to joules since R is usually given in units of Joules (J).

1 calorie = 4.184 joules

So, 0.075 calories = 0.075 * 4.184 joules = 0.3138 joules

Now, let's substitute the given values into the equation:

0.3138 Joules = (0.5 * R) * (atomicity)

To find the atomicity, we need to know the value of R. The value of the molar gas constant R is approximately 8.314 J/(mol·K).

Let's assume the gas behaves ideally and use this value of R:

0.3138 Joules = (0.5 * 8.314 J/(mol·K)) * (atomicity)

Simplifying the equation:

0.3138 Joules = 4.157 J/(mol·K) * (atomicity)

Now, let's isolate the atomicity:

atomicity = 0.3138 Joules / (4.157 J/(mol·K))
atomicity = 0.3138 Joules * (mol·K) / 4.157 J

Simplifying further, we obtain:

atomicity ≈ 0.0753 ≈ 0.075

Therefore, the atomicity of the gas is approximately equal to 0.075.