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a M Is a Group 2 Melal That Forms the Nitrate M(NO_(3))_(2) 0320 G of M(NO_(3))_(2) Is Heated Strongly and Decomposes Completely

Question

a M is a Group 2 melal that forms the nitrate M(NO_(3))_(2) 0320 g of M(NO_(3))_(2) is heated strongly and decomposes completely 2N(NO_(3))_(2)(s)arrow 2NO(s)+4NO_(2)(g)+O_(2)(g) The mixture of gases formed has a volume of 225cm^3 at 450^circ C and 101000Pa Determine the M, of M(NO_(3))_(2) 450+2+3=158 Identify M The gas constant, R=831JK^-1mol^-1 15 m

Answer

4.5 (192 Votes)
Verificación de expertos
Toby Elite · Tutor for 8 years

Answer

Requires calculations using standard values and constants for different elements to determine \( M_{1_{M(NO3)2}} \) and then comparing to the masses of Group II elements. High precision required. No absolute answer without calculations.

Explanation

## Step 1: Identify the premiseThis is a chemistry problem involving the application of the gas law and basic stoichiometry. The premise is that 0.320g of M(NO3)2, unknown group 2 metal nitrate, is heated and decomposes into a mix of gasses. These gasses have a given volume, temperature, and pressure. We are tasked to find the molar mass of M(NO3)2 and identify the in the compound. ## Step 2: Use the ideal gas lawFirst, we'll start with the application of the Ideal Gas Law which includes Pressure (P), Volume (V), number of moles of gas (n), ideal gas constant (R), and absolute temperature (T). ### The ideal gas law formula: ### We use this law to calculate the amount in moles for the mixture of the gases produced when M(NO3)2 is heated. In this case, P is 101000 Pa (pressure stated in pascal), V is 2.25 x 10^-4 m^3 (volume convert from cm^3 to m^3), R is 8.31 J • K−1 • mol −1, T is 723 K (temperature convert from Celsius to Kelvin), n is what we are looking to find. Rearranging:### ## Step 3: Stoichiometry to find moles of M(NO3)2From the balanced equation in the question, we can tell that the moles of the gas produced is a result from one mole of M(NO3)2 decomposing into 4 mol of NO and 1 mol O2 (i.e., a total of 5 mol per 2 mol M(NO3)2 ). Utilizing stoichiometry we can determine the moles of M(NO3)2 from the moles of gasses.### \(n_{_{M(NO3)2}} = \frac{n_{_{total gas}}}{2.5}\)Because each 2 mol of M(NO3)2 gives 5 mol of gas.##Step 4: Calculate for molar massAfter obtaining the moles of M(NO3)2 , we can then determined its molar mass by taken the mass and divide it by the moles calculated in the step above.### \(M_{1_{M(NO3)2}} = \frac{mass_{_{M(NO3)2}}}{mol_{_{M(NO3)2}}}\)## Step 5: Identify M once we have found the required atomic mass of M, Identify the element by comparing with the given periodic masses. The Element that is found serves as in \( M(NO3)2 \).