The root mean square speed of hydrogen molecules of an ideal hydrogen gas kept in a gas chamber at `0^(@)C` is 3180 m/s. The pressure on the hydrogen gas is ………..
(Density of hydrogen gas is `8.99xx10^(-2)kg//m^(3)`, 1 atmosphere= `1.01xx10^(5)N/m^(2)`

Answer

To find the pressure of hydrogen gas given the root mean square speed (vrms), density, and temperature, we can follow these steps:

### Step 1: Understand the relationship between vrms, pressure, and density
The root mean square speed (vrms) of an ideal gas can be expressed using the formula:

\[ v_{rms} = \sqrt{\frac{3P}{\rho}} \]

Where:
- \( P \) is the pressure of the gas,
- \( \rho \) is the density of the gas.

### Step 2: Rearrange the formula to find pressure
We can rearrange the formula to solve for pressure \( P \):

\[ P = \frac{1}{3} \rho v_{rms}^2 \]

### Step 3: Substitute the known values
We know:
- \( v_{rms} = 3180 \, \text{m/s} \)
- \( \rho = 8.99 \times 10^{-2} \, \text{kg/m}^3 \)

Now substitute these values into the formula:

\[ P = \frac{1}{3} \times (8.99 \times 10^{-2}) \times (3180)^2 \]

### Step 4: Calculate \( v_{rms}^2 \)
First, calculate \( v_{rms}^2 \):

\[ v_{rms}^2 = (3180)^2 = 10112400 \, \text{m}^2/\text{s}^2 \]

### Step 5: Calculate pressure \( P \)
Now substitute \( v_{rms}^2 \) back into the pressure formula:

\[ P = \frac{1}{3} \times (8.99 \times 10^{-2}) \times 10112400 \]

Calculating this gives:

\[ P = \frac{1}{3} \times 908,999.76 \approx 302,999.92 \, \text{Pa} \]

### Step 6: Convert pressure from Pascals to atmospheres
To convert from Pascals to atmospheres, use the conversion factor \( 1 \, \text{atm} = 1.01 \times 10^5 \, \text{Pa} \):

\[ P_{atm} = \frac{302999.92}{1.01 \times 10^5} \approx 3.00 \, \text{atm} \]

### Final Answer
The pressure on the hydrogen gas is approximately **3.00 atm**.

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