Calculate the number of molecules in 540cm square of hydrogen gas(H=1,O=16,Avogadro's constant=6.02 x 10 raised to power 23)
To calculate the number of molecules in a given amount of substance, we need to follow the steps below:
Step 1: Write down the given information:
- Area = 540 cm²
- Hydrogen (H) atomic mass = 1
- Avogadro's constant (NA) = 6.02 x 10^23 molecules/mol
Step 2: Calculate the number of moles of hydrogen gas using the given area:
- Since we are given an area, we need to convert it into volume.
- Assuming the hydrogen gas is at STP (Standard Temperature and Pressure), we can use the ideal gas law equation to find the volume.
- 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 (8.314 J/(mol·K)), and T is the temperature (in Kelvin).
- Since the pressure and temperature are not specified, we can assume they are at standard conditions, which are 1 atm and 273.15 K.
- Rearranging the ideal gas law equation to solve for V, we have V = nRT / P.
- At STP, the pressure is 1 atm, which is equivalent to 101.325 kPa.
- The temperature is 273.15 K.
- The ideal gas constant is approximately 0.0821 L·atm/(mol·K).
- Plugging in the values, we have V = n * 0.0821 * 273.15 / 101.325.
- Since we are given the area of the hydrogen gas, we can assume it forms a cube, with each side equal to the square root of the area.
- The volume of the cube is V = (side length)³.
- Plugging in the values, we have (side length)³ = n * 0.0821 * 273.15 / 101.325.
- Rearranging the equation to solve for n, we have n = [(side length)³ * 101.325] / [0.0821 * 273.15].
- Convert the side length from centimeters to liters since we are using the ideal gas constant in liters.
Step 3: Calculate the number of molecules using the number of moles:
- The number of molecules in a given substance can be calculated by multiplying the number of moles by Avogadro's constant (NA).
Let's apply these steps to the given information:
Step 1: Given information:
- Area = 540 cm²
- Hydrogen (H) atomic mass = 1
- Avogadro's constant (NA) = 6.02 x 10^23 molecules/mol
Step 2: Calculate the number of moles of hydrogen gas:
- Calculate the side length of the cube: side length = sqrt(540 cm²) = 23.237 cm
- Convert the side length to liters: side length = 23.237 cm³ * (1 L / 1000 cm³) = 0.023237 L
- Calculate the number of moles: n = (0.023237 L)³ * 101.325 kPa / (0.0821 L·atm/(mol·K) * 273.15 K)
- This gives us the number of moles of hydrogen gas in the given volume.
Step 3: Calculate the number of molecules:
- Number of molecules = n * Avogadro's constant
- Substitute the calculated value of n and Avogadro's constant to get the final answer.
By following these calculation steps, you can find the number of molecules in 540 cm² of hydrogen gas.